FOXBOROUGH, Mass. — Step One is out of the way for the New England Patriots.

Again.

“I know we have big goals every year for our team. This is the one that’s the first one to get and it’s great to be able to do it against a team that we lost to earlier in the year,” New England quarterback Tom Brady said after the Patriots clinched their sixth straight AFC East title by shaking off a flat first half to cruise to a 41-13 victory over the Miami Dolphins on Sunday.

“We had a great opportunity to go out there and play a lot better than we did the last time [the season opener against Miami], so … it was great to win. It’s a great feeling. That’s why we play and I’ve been very fortunate to be a part of an organization where that’s really what matters most.”

Cornerback Kyle Arrington romped 62 yards and somersaulted into the end zone with a blocked field early in the game, and the Patriots scored a franchise-record 24 points in the third quarter to wrap up their 11th division crown in the last 12 years.

In avenging the 33-20 opening loss to Miami, the Patriots (11-3 with nine wins in the last 10 games) can ensure home-field advantage throughout the AFC playoffs with wins in their final two games. They are 7-0 at home this season.

The win kept the Dolphins (7-7) from becoming the first division opponent to sweep a season series from the Patriots since 2000 while also moving New England to 24-1 at home in December since 2003.

The Patriots have won 17 straight home games against teams in their division, the second-longest such streak in the NFL since 1970.

Kicker Stephen Gostkowski kicked a 35-yard field goal in the third quarter to become the Patriots’ all-time scoring leader, passing Adam Vinatieri. He kicked another field goal in the fourth quarter.

Brady, clinching his NFL-record 12th division title, overcame a shaky first half with two second-half touchdown passes as the Patriots ran up a 27-0 second-half rout.

“I just didn’t think we played the way we needed to play,” Patriots coach Bill Belichick said of the first half. “It was a good second half.”

Miami quarterback Ryan Tannehill hit wide receiver Mike Wallace with a 50-yard bomb on the first play of the day. But linebacker Jamie Collins then blocked a 41-yard field goal by Caleb Sturgis and Arrington, who would leave in the second quarter with a hamstring injury, scooped it up and returned it for a touchdown.

Tight end Rob Gronkowski, who caught one of the touchdown passes, had three catches for 96 yards, clearing the 1,000-yard receiving mark for the second time in his career. Julian Edelman caught seven passes for 88 yards and a touchdown and fellow wide receiver Brandon LaFell had six catches for 66 yards.

Running backs Shane Vereen and LeGarrette Blount scored rushing touchdowns for the Patriots, while Tannehill threw a 32-yard touchdown pass to Wallace, and Sturgis hit two field goals for the Dolphins, who were plagued by mistakes all day as their almost-gone playoff hopes dwindled further.

Brady, who had a 41.5 passer rating while hitting 8 of 15 first-half passes, finished 21 of 35 for 287 yards, an interception and a 93.4 rating. He also had a 17-yard scramble that led to a touchdown, taking a heavy hit rather than sliding.

Tannehill, sacked four times, was 29 of 47 for 346 yards and two picks.

What the Patriots said:

“It’s flattering, very flattering. Curly was one of the great founders really of the National Football League … It’s very flattering to be put in his category.” – head coach Bill Belichick after tying Curly Lambeau for fourth place on the all-time wins list

What the Dolphins said:

“Coach came in and gave a really good speech at halftime; guys were pumped up. The other team just came out and outplayed us. It fell apart in the second half. They beat us up. They made more plays than we did. It’s just unacceptable.” – guard Mike Pouncey

What we learned about the Patriots:

1. The Patriots can get ticked off when they play a poor first half. A dreadful final minute capped a flat first half and had the Patriots ahead by a point at the break, with the offense again sputtering. But then came a club-record 24-point third quarter and a 27-0 second-half run that easily put the Dolphins away.

2. Running back Jonas Gray lives. A club-record four touchdowns and the cover of Sports Illustrated quickly turned to dust because the rookie arrived late for practice. He had basically been buried from that point on, but on Sunday, he rushed for 62 yards and caught a pass for 7 more in the division-clinching win. It gives him time to again become a factor going forward into the final two games of the regular season and the playoffs.

–QB Tom Brady had a big 17-yard run deep in Miami territory to set up a touchdown, and he took a heavy hit on the play and shook off a slow first half to post another good game. He had only a 41.5 passer rating in the first half but finished with a 93.5. He wound up 21 of 35 for 287 yards, two touchdowns and an interception and added to his own record with his 12th division title. Brady, who said he was still angry about the first half when he decided not to slide on the run, instead taking a heavy hit from safety Walt Aikens. “We were all [ticked] off at halftime,” he said. Said Aikens: “He got up, and he was like, ‘Woo!’ he was excited.”

–TE Rob Gronkowski caught three passes for 96 yards and a touchdown Sunday, going over the 1,000-yard mark for the second time in his career. “He’s a big target for me,” said Brady. “He makes it easy for me. He’s awesome.” Gronkowski, talking about the team’s mood when leading by a point at the half, said, “We just knew we could play better. We were terrible in the first half as a whole and as myself. We just had to go out there and execute and play together as an offense.”

–K Stephen Gostkowski kicked a pair of field goal and five extra points Sunday, allowing him to pass Adam Vinatieri and become the Patriots’ all-time leading scorer with 1,165 points. “I’ve been really lucky,” said coach Bill Belichick. “Adam, Steve, Shayne (Graham) when he came in here and didn’t miss a kick the half a year he was here, or whatever it was. …Steve, those are big shoes to follow there with Adam, but he’s never blinked.” Said Gostkowski: “Something like that doesn’t really set in. I’ve said this before but any accomplishment that I make will be something that I’ll look back on when I’m done playing, and be excited about and probably brag to my kids and grandkids about, hopefully. It was cool. It was a special game for me. It’s my son’s birthday tomorrow and my whole family is in town.”

–RB Jonas Gray re-emerged from the doghouse he moved into by showing up late for a practice. He contributed to the latest win. Gray, who scored four touchdowns the last time he put in any serious time, ran for 62 yards on 11 carries and caught a pass from 7 yards.

–DE Rob Ninkovich sacked Ryan Tannehill in the fourth quarter. It was Ninkovich’s eighth sack of the season, making him the first Patriot with at least eight sacks in three straight seasons since Andre Tippett did it from 1985-87.

What we learned about the Dolphins:

1. This team just makes too many mistakes to be a legitimate playoff team. Yes, at 7-7 the Dolphins were still mathematically alive, but dropped passes and other mistakes continue to get in the way and will be the key reason they’ll be watching come playoff time — and why coach Joe Philbin’s coaching tenure may well be coming to an end.

2. Quarterback Ryan Tannehill has a bright future as a quarterback. He threw for 346 yards and a touchdown Sunday and the numbers could have been better had a couple of balls been held or an official made an interference call that should have been made. He’s not Tom Brady, but that doesn’t mean he can’t play.

–QB Ryan Tannehill started his day with a 50-yard completion to wide receiver Mike Wallace and could have had better numbers had it not been for mistakes and a missed call. He finished 29 of 47 for 346 yards, a touchdown and two interceptions. He was sacked four times in the loss. Asked about coach Joe Philbin being in trouble, Tannehill said, “It’s not on Coach. Coach puts us in a good position. [He] prepares us well and the fact of the matter is we’re not out there making the plays. So you can’t put that on Coach. He’ll take responsibility, but he’s not the one out there messing up the plays and not executing. So when you take a real look at it, it’s on the players.”

–WR Jarvis Landry, who came into the game leading NFL rookie receivers in receptions, had another strong game. He caught eight passes for 99 yards and also had a 32-yard punt return. He has 71 catches for the season.

–LB Justin Trusnik, getting the start because of injuries, batted a first-quarter Tom Brady pass up into the air and came down with it for his first career interception.

–WR Mike Wallace made a one-hand catch of a 32-yard pass from Ryan Tannehill that was originally called incomplete before being reversed. Wallace had seven catches for 104 yards and showed his frustration after the game. “Same as last year,” he said. “We had the season in our hands, we could do something about it and we dropped the ball. Again.”