Raiders deal stunning blow to 49ers’ playoff hopes

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Maybe the Raiders don’t need Jim Harbaugh after all.

After a week of speculation that the 49ers could trade their head coach, or that he might even end up with the Raiders next season, Harbaugh watched Sunday afternoon as his team was thoroughly outplayed by the until-then 1-11 team from the East Bay.

Rookie Derek Carr threw three touchdown passes — one to Donald Penn, who’s normally the left tackle — and Oakland gave its fans bragging rights with a 24-13 win over San Francisco at a sold-out Coliseum.

“We knew how important this game was to the city,” said Raiders defensive tackle Antonio Smith, who had two sacks.

The 49ers’ defense had no answer for short passes to tight end Mychal Rivera and fullback Marcel Reece, and on offense, quarterback Colin Kaepernick had no touch to make short passes. His attempts downfield often sailed by receivers with impressive velocity, as he finished 18-for-33 for 174 yards with a touchdown and two interceptions.

“I have to play better,” Kaepernick said. “I haven’t played well.”

San Francisco’s last gasp came when Phil Dawson missed a 47-yard field-goal attempt with 5:03 left in the game. The 49ers’ playoff chances are pretty much dead with a 7-6 record and a trip to Seattle next on the calendar.

Harbaugh was asked about his future, and was as open as his offense had been.

Oakland Raiders' Mychal Rivera celebrates his 4th quarter touchdown reception with Latavius Murray during 24-13 win over San Francisco 49ers in NFL game at O.co Coliseum in Oakland, Calif., on Sunday, December 7, 2014. less Oakland Raiders' Mychal Rivera celebrates his 4th quarter touchdown reception with Latavius Murray during 24-13 win over San Francisco 49ers in NFL game at O.co Coliseum in Oakland, Calif., on Sunday, December ... more Photo: Scott Strazzante, The Chronicle Photo: Scott Strazzante, The Chronicle Image 1 of / 62 Caption Close Raiders deal stunning blow to 49ers’ playoff hopes 1 / 62 Back to Gallery

“My priorities are No. 1, winning football games, No. 2, the welfare of our players, coaches and our staff,” Harbaugh said, “and lastly is what my personal professional future is …

“It falls on me if we don’t win these games.”

Oakland is 2-11, but fans are skipping gleefully after beating the Bay Area’s other team. And general manager Reggie McKenzie is probably doing a little dance himself after a win that might end speculation about whether owner Mark Davis will bring him back next year.

After all, McKenzie drafted Carr and linebacker Khalil Mack — who had two sacks — this year, and paying McKenzie for two more years for not being his general manager wasn’t high on Davis’ list anyway.

The Raiders were coming off a 52-0 loss to the Rams in St. Louis, but interim head coach Tony Sparano wouldn’t admit they spent that whole week preparing for this game.

Sparano got a Gatorade shower from his players, unusual for 2-11 teams, and he was dripping admiration afterward.

“Really proud of the guys ... they’re resilient,” Sparano said. “I’m really happy for our fans, I’m really happy for our owner, GM, but mostly happy for the kids in that (locker) room. They fought their tails off for me.”

Carr was better than Kaepernick from the get-go. On the game’s first play, Kaepernick rolled left and his pass for Michael Crabtree sailed well past the receiver and into the accepting arms of Raiders safety Brandian Ross.

The Raiders, however, got only three points off that turnover and didn’t really get their offense going until the second quarter. That’s when, down 7-3, Carr led Oakland on an 11-play, 74-yard drive that ended with a 3-yard pass to Penn.

Carr faked a handoff to Latavius Murray and then threw a low pass that the 340-pound former Los Angeles high school basketball player reached down and grabbed. Penn took a big shot from safety Eric Reid as he scored, but shook it off and then made fans’ day/scared the bejesus out of them when he jumped into the Black Hole.

After San Francisco regained the lead 13-10 on two Dawson field goals, Carr hit Reece for a 9-yard touchdown with 4:09 left in the third quarter. Reece lined up wide left and easily beat cornerback Dontae Johnon on a slant route.

Carr then hit Rivera for a 5-yard touchdown pass with 10:39 left in the game, as Rivera posted up Niners cornerback Leon McFadden and Carr made a nice, high entry pass.

Rivera finished with a career-high 109 yards on seven catches, and Reece added 64 yards on seven catches.

No 49ers receiver had more than 56 yards; Kaepernick didn’t have much time or accuracy. The Raiders had a season-high five sacks and Smith said they were “definitely in his head.” That, along with Kaepernick’s refusal to run.

“We got a lot of quarterback drop-back passes,” Smith said. “Whenever you have that, that’s when your pass rush is eating.”

The Raiders, like the Seahawks on Thanksgiving, are stuffed and content. The 49ers sure look like they are cooked.

Vic Tafur is a San Francisco Chronicle staff writer. E-mail: vtafur@sfchronicle.com Twitter: @VicTafur

3 notables

Derek Carr: The best quarterback on the field by far Sunday. The rookie bounced back from a 52-0 loss to the Rams by throwing three touchdown passes, thanks in part to an offensive line that gave him plenty of time.

Colin Kaepernick: Hurt the Raiders with runs of 17 and 16 yards on a field-goal drive to end the half, and then didn’t run the ball again. Quarterback’s accuracy issues are becoming greater. Was he still seeing 11 Richard Shermans out there?

Mychal Rivera: The second-year tight end had a career-high 109 yards receiving and interim head coach Tony Sparano said his chemistry with Carr is a bright sign for the future.

—Vic Tafur