OAKLAND, Calif. — To Oakland Raiders interim coach Tony Sparano, it was clear what the San Francisco 49ers’ defensive game plan was Sunday.

The 49ers crowded the line of scrimmage, tried to take away the run, and dared Raiders rookie quarterback Derek Carr to beat them, Sparano said.

That’s exactly what Carr did.

Carr passed for 254 yards and three touchdowns, leading the Raiders to a stunning 24-13 victory over the 49ers and delivering a severe blow to their Bay Area rivals’ playoff hopes.

Carr completed 22 of 28 passes, posted a passer rating of 140.2 and didn’t throw an interception. What’s more, he decisively outplayed 49ers quarterback Colin Kaepernick, who had another rough game. Kaepernick completed 18 of 33 passes for 174 yards and one touchdown. He was intercepted twice, sacked five times and had a 54.4 passer rating.

“I honestly thought Derek played really well tonight,” Sparano said. “Best game? I don’t know. I think he threw really well thought. We had a lot of (49ers) down there in the box today, and they didn’t want us to run the ball. They obviously wanted to see whether or not we could beat them throwing the football, and Derek was able to do that.”

Raiders tight end Mychal Rivera caught seven passes for a career-high 109 yards with one score.

Fullback Marcel Reece caught seven passes for 64 yards and a touchdown, and offensive tackle Donald Penn caught his third career touchdown pass.

The Raiders (2-11) were coming off a 52-0 loss to the St. Louis Rams, but they won for the second time in three games.

The 49ers (7-6) lost their second game in a row, as they fell 19-3 to the Seattle Seahawks on Thanksgiving. San Francisco dropped three games behind the first-place Arizona Cardinals (10-3) in the NFC West and lost critical ground in the wild-card race.

“There’s no surrendering,” 49ers coach Jim Harbaugh said.

49ers wide receiver Michael Crabtree caught a game-high nine passes for 56 yards.

The 49ers snapped a 10-10 tie early in the third quarter, settling for Phil Dawson’s 20-yard field after stalling at Oakland’s 2-yard line. But the Raiders responded with back-to-back 80-yard touchdown drives.

“It was nice. It was real nice,” Carr said. “I know the kind of talent we have and the kind of team we have. We haven’t been able to put it together obviously throughout the season. We’re young and we’re continuing to work hard and listen to our coaches and the game plan, knowing it in and out. And I felt for the first time there weren’t the little detail mistakes that have ruined it.”

Carr capped an eight-play, 80-yard drive with a 9-yard scoring strike to Reece, giving Oakland a 17-13 lead with 4:08 remaining in the third period. Carr, getting great pass protection, completed all five of his throws on the drive for 71 yards.

The Raiders forced a punt and kept attacking. This time they needed 11 plays to cover 80 yards and took a 23-13 lead on Carr’s 5-yard scoring pass to Rivera with 10:39 remaining. Carr went 6-for-7 for 83 yards on the drive.

“I think he did a great job of extending the play,” 49ers safety Eric Reid said of Carr. “He got outside the pocket and bought his receivers some time and then he delivered the ball, and we’ve just got to make more plays.”

The 49ers drove to Oakland’s 25, but on third-and-8, Raiders defensive tackle Antonio Smith sacked Kaepernick for a 4-yard loss. Dawson then hooked his 47-yard field attempt wide left with 5:03 remaining. Smith and linebacker Khalil Mack each had two sacks, and linebacker Benson Mayowa had one.

“Whenever you get pressure on the quarterback, you know you’re in his head,” Smith said. “I think early on he was having success breaking out of the pocket and making some big runs, so that kind of gave him confidence. But once we kind of closed the front down and stopped him from breaking open up the middle, it just made it that much easier to get him down.”

Oakland sealed the victory when free safety Charles Woodson picked off a Kaepernick pass, giving Oakland a first down at the 49ers’ 28 with 2:36 remaining.

“I have to play better,” Kaepernick said.

What the Raiders said:

“It was great, man. It’s the way you expect this game to be. Our crowd was in it from the jump, and a lot of that was because of what we did out there on the field — coming out early, getting a turnover, the offense being able to drive the ball down the field, put points up. It was a great game from start to finish, and it was great for the fans.” — Safety Charles Woodson.

What the 49ers said:

“We got to win out. It’s the only chance we have. Anything can happen.” — Safety Eric Reid.

What we learned about the Raiders:

1. Even if the Raiders get the top pick in the 2015 draft, they won’t need to even consider drafting a quarterback. Derek Carr is establishing himself as the quarterback of the present and future. He completed 22 of 28 passes for 254 yards and three touchdowns Sunday against the 49ers. He posted a career-high 140.2 passer rating and didn’t throw an interception in arguably his best game of the season.

2. The Raiders refuse to quit, no matter how many reasons they have to do exactly that. Oakland was coming off a humiliating 52-0 loss to the St. Louis Rams, but it played as if a playoff berth were on the line Sunday. “Really proud of the guys in that room,” Raiders interim coach Tony Sparano said. “It took a lot of courage to do what they did today, a lot of courage. I love that group in there. They’re resilient.”

–TE Mychal Rivera caught seven passes for a career-high 109 yards and one touchdown Sunday against San Francisco, cracking the 100-yard receiving mark for the first time in his career. He is the first Raiders tight end with a 100-yard receiving game since Brandon Myers on Dec. 2, 2012, against Cleveland.

–QB Derek Carr completed 22 of 28 passes for 254 yards and three touchdowns Sunday in a 24-13 victory against the 49ers. Carr, who did not throw an interception, posted a career-high 140.2 passer rating — the sixth-best mark by an NFL rookie, with a minimum of 20 attempts, since 1960.

–FS Charles Woodson had his 59th career interception Sunday, picking off a pass by 49ers QB Colin Kaepernick late in the fourth quarter. He ranks 11th on the NFL’s all-time interception list. Woodson led the Raiders with eight tackles, seven of them solo.

What we learned about the 49ers

1. Quarterback Colin Kaepernick continued to regress, but his make-shift offensive line deserves some of the blame. Kaepernick, who was sacked five times Sunday in a 24-13 loss to the Raiders, has been sacked a league-high 43 times for the season. Starting right tackle Anthony Davis missed his second consecutive game with a concussion, and starting left guard Mike Iupati left the game late in the first half with a hyperextended elbow. Starting center Daniel Kilgore went on injured reserve Oct. 25, with rookie Marcus Martin taking his place. The line is undermanned and, at times, overmatched.

2. After making three straight trips to the NFC title game, the 49ers will need a miracle just to reach the playoffs this season. At 7-6, they are two games behind the Seattle Seahawks, Detroit Lions and Dallas Cowboys in a battle for the NFC’s two wild-card berths. “We play this game for one purpose, and that purpose is to go to the Super Bowl,” tight end Vernon Davis said. “So we just have to continue to play for what we’re playing for.”

–QB Colin Kaepernick continued to struggle Sunday. He completed 18 of 33 passes for 174 yards and one touchdown in a 24-13 loss to the Raiders. Kaepernick was intercepted twice and sacked five times. He posted a 54.4 passer rating. In his past two games — losses to Seattle and Oakland — Kaepernick passed for a total of 295 yards and one touchdown.

–WR Michael Crabtree caught a game-high nine passes but for only 56 yards Sunday against the Raiders. He averaged 6.2 yards per catch and didn’t get in the end zone. Crabtree has 60 catches for 633 yards and four touchdowns on the season.

–OLB Ahmad Brooks missed a team meeting earlier in the week and did not play Sunday against Oakland, although he suited up. Brooks had started 60 consecutive games. Brooks said he was never told by his coaches that he wouldn’t start or play. “I’m not here to point fingers,” Brooks said. “I’m not the only one that’s ever missed anything. Of course, there’s been other people that’s missed or been late. But I’m not going to point fingers. I own up to my responsibilities. I wasn’t there. They made a decision. It is what it is. We’ll just go forward from there.”