SANTA CLARA, Calif. -- The New York Jets trailed the San Francisco 49ers 17-3 at halftime Sunday and appeared headed to their fifth consecutive loss.

Backup running back Bilal Powell and the Jets had other ideas.

Powell rushed for 145 yards and two touchdowns on 29 carries, including a 19-yard score with 8:35 left in overtime, lifting the Jets to an improbable 23-17 victory at Levi's Stadium..

The Jets (4-9) scored 20 unanswered points to end their four-game losing streak and hand San Francisco (1-12) its 12th straight loss, an ongoing franchise record.

Powell took over after Jets starting running back Matt Forte injured a knee early in the first quarter.

"If it wasn't for him, I don't know if we win this game," Jets coach Todd Bowles said. "He singlehandedly, from my point of view, broke every tackle he could break. He caught every ball. He ran, he blocked. He did everything and had an outstanding effort."

Powell fell 4 yards shy of matching his career-high rushing mark set in 2013 against the Buffalo Bills. He gained 121 of his rushing yards and scored both TDs after halftime. Powell finished the game with five catches for 34 yards.

"Whenever my number is called, I just try to step up and take advantage of my opportunity," Powell said. "When Matt went down, I was well-prepared like I am each and every week."

Jets second-year quarterback Bryce Petty made his second career start and completed 23 of 35 passes for 257 yards and one interception. He was sacked six times, all in the first half.

"First half was probably about as ugly as I could play," Petty said. "I came out a little bit more nervous than I thought I was going to be. Hats off to the team for sticking with me. We just kept fighting, kept fighting and plugging away."

Carlos Hyde carried 17 times for a career-high 193 yards and caught a 7-yard touchdown pass for the 49ers. Hyde carried seven times for 141 yards in the first half when he had the two longest runs of his career -- 47 yards in the first quarter and 43 in the second.

San Francisco quarterback Colin Kaepernick completed 15 of 26 passes for 133 yards. He was 4 of 11 for 17 yards in the second half and overtime.

"We have to do a better job finishing," Kaepernick said. "There's a lot of plays and a lot of opportunities all over the field that we have to be able to take advantage of."

Jets kicker Nick Folk connected from 30 yards with 6:28 left in the third quarter, cutting San Francisco's lead to 17-6.

With 5:04 remaining in the game, Powell scored on a 5-yard run, capping a 15-play, 66-yard drive. Petty ran for two points, making it 17-14.

After forcing a punt, the Jets took over on their 35-yard line with 2:35 left. They marched to the 49ers 32, and Folk kicked a 50-yard field goal as the Jets pulled even with 38 seconds left in regulation.

San Francisco took the opening kick in overtime, but Hyde was stopped for no gain on fourth-and-1 at the New York 36-yard line. Defensive linemen Muhammad Wilkerson and Deon Simon shared credit for the tackle.

"That's a play we've been running all game," Hyde said. "The Jets just played good defense right there. They did a good job filling up all the holes."

Three plays later, Petty scrambled to his left and hit Robby Anderson for 26 yards to the San Francisco 25. On third-and-4 from the 19, Powell took it the rest of the way.

"I knew he was going to put it up to me," said Anderson, who had six catches for 99 yards. "I was just waiting for the ball. I knew it was going to be a big play."

The 49ers took control early, building a 14-point halftime lead as they outgained the Jets 279-118.

On the game's second play from scrimmage, 49ers cornerback Jimmie Ward cut in front of Jets wide receiver Quincy Enunwa along the right sideline and intercepted Petty's pass. On first down, Kaepernick hit Hyde for a touchdown and a 7-0 lead with 13:57 left in the first quarter.

The 49ers extended their lead to 14-0 on running back Shaun Draughn's 4-yard touchdown run three minutes later.

The Jets cut San Francisco's lead to 14-3 with 7:28 left in the first half on Folk's 36-yard field goal. San Francisco's Phil Dawson, who missed from 44 and 48 yards on his first two field-goal attempts, hit from 47 with 5:45 remaining in the half.

NOTES: San Francisco C Daniel Kilgore left the game late in the first quarter with a leg injury and did not return. ... 49ers OT Joe Staley (hamstring) was inactive, ending his streak of 100 consecutive starts, including eight in the playoffs. He hadn't missed a game since being sidelined for the final seven in 2010. ... Jets starting CB Buster Skrine left the game against early in the second quarter with a head injury and did not return. ... 49ers starting WR Torrey Smith sustained a concussion with 3:22 left in the third quarter while trying to make a catch and landing hard. He was carted to the locker room and did not return. ... San Francisco starting TE Vance McDonald sustained a shoulder injury in the second quarter and did not return. ... Jets starting TE Brandon Bostick left the game early in the third quarter with an ankle injury and did not return.