OAKLAND, Calif. -- The last time the Raiders made the playoffs was after the 2002 season, but Oakland took another step Sunday in its quest to end that drought.

Quarterback Derek Carr threw for 333 yards and a career-high-tying four touchdowns, leading the Raiders to a 34-20 victory against the New York Jets at the O.co Coliseum.

The Raiders improved to 4-3 and are tied with the Jets (4-3) atop the early wild-card standings in the AFC. Oakland already has as many wins this season as it recorded all of last season.

"We want to be expected to win," Raiders free safety Charles Woodson said. "When we watch the media, the TV guys, whatever, I want them to pick the Raiders.

"It's a big win for us, beating a good team. ... It speaks to what we're building and where we're trying to go."

Raiders running back Latavius Murray gained 113 yards on 20 carries against a New York defense that entered the game ranked first against the run in the NFL.

"We've been hearing it all week, that's what they do is stop the run," Murray said. "We definitely took that as a challenge and made sure we dictated what happened out there in the running game."

Carr completed 23 of 36 passes with no interceptions and had his fourth career 300-yard passing game, including three this season. Raiders wide receiver Andre Holmes caught two touchdown passes. Running back Taiwan Jones scored on a 59-yard pass, and wide receiver Michael Crabtree scored on a 36-yarder. Crabtree caught seven passes for 102 yards.

Jets running back Chris Ivory rushed for only 17 yards on 15 carries against an Oakland defense that was ranked third in the NFL against the run.

"That's a testament to the guys," said Raiders defensive end Khalil Mack, who had three tackles for losses. "We've been working hard."

Jets starting quarterback Ryan Fitzpatrick tore ligaments in his left thumb with 11:06 left in the first quarter at the end of a 14-yard scramble when he was tackled by Woodson. He left the game and took only two more snaps, those coming late in the fourth quarter after backup quarterback Geno Smith was shaken up on a sack.

"He's going to get MRIs tomorrow, and we'll go from there," Jets coach Todd Bowles said of Fitzpatrick.

Smith made his season debut and first appearance since Dec. 28, 2014, against Miami. Smith, the Jets' starter the previous two seasons, sustained a broken jaw on Aug. 11 when then-teammate IK Enemkpali punched him during an argument in the locker room.

Smith, who had been active since Week 3 against Philadelphia, completed 27 of 42 passes for 265 yards and two touchdowns with one interception. He threw a 4-yard touchdown strike to wide receiver Eric Decker in the third quarter and a 1-yard scoring throw to tight end Kellen Davis in the fourth.

"I felt ready," Smith said. "I've been getting enough reps in practice and doing a bunch in the classroom, so we were on the same page."

Smith was injured with 54 seconds left in the fourth quarter on a sack when he was hit in the abdomen. His head snapped back and hit the turf hard as he landed. Fitzpatrick, the Jets' only other active quarterback, returned to the game for two plays, despite his thumb injury. Smith returned after that and finished the game.

Earlier in the half, Smith took a huge hit on his left shoulder from Raiders cornerback David Amerson along the right sideline at the end of a 29-yard run. Smith said he was not sure if he would miss time because of his injuries.

"We did X-rays on my shoulder," Smith said. "My abdomen feels good. Still got to monitor everything and get in the treatment this week."

Jets wide receiver Brandon Marshall caught nine passes for 108 yards despite battling ankle and toe injuries.

Woodson had his fifth interception of the season and 65th of his career, moving him into a tie for fifth place on the NFL's all-time list with Ken Riley.

The Raiders built a 30-3 halftime lead last week in their 37-29 win at San Diego, and they got off to another hot start Sunday.

Carr marched the Raiders to touchdowns on their first three drives of the game as they built a 21-3 advantage and led 21-6 at halftime. He threw three first-half touchdown passes, hitting Holmes for 5 yards, Crabtree for 36 yards and Holmes again for 49 yards. Carr completed 14 of 18 passes for 178 yards in the first half.

"Us just doing our job," Carr said of the key to Oakland's fast starts. "There's no superhuman anything."

Oakland opened the second half with a six-play, 93-yard touchdown drive capped by Carr's 59-yard scoring pass to Jones, increasing the lead to 28-6.

NOTES: Jets C Wesley Johnson started in place of Nick Mangold (neck), who was inactive. ... Jets SS Calvin Pryor (ankle) was inactive. Dion Bailey started in his place. ... Raiders LB Korey Toomer, who was signed Saturday off the practice squad, was active against the Jets. ... Jets backup CB Dexter McDougle sustained an ankle injury in the first half.