OAKLAND, Calif. -- The Kansas City Chiefs trailed Oakland 20-14 early in the fourth quarter Sunday, and their five-game winning streak was in serious jeopardy.

The Chiefs needed a big play. They got three of them, the biggest from former Raiders safety Tyvon Branch.

Branch returned an interception 38 yards for a touchdown with 3:14 left to play, and the Chiefs held on for a 34-20 victory against the Raiders at the O.co Coliseum.

The Chiefs (7-5) picked off three passes from Oakland quarterback Derek Carr in the fourth quarter as they solidified their strong position in the AFC wild-card race.

Linebacker Josh Mauga and rookie cornerback Marcus Peters, who grew up in Oakland, also had interceptions and long returns, setting up touchdowns in the fourth quarter.

"It's huge," Branch said of the turnovers. "We're on a roll right now. We got a goal and our leaders and our coach make sure we stay focused on that goal."

Chiefs wide receiver Jeremy Maclin caught nine passes for 95 yards and two touchdowns, both in the fourth quarter. Kansas City quarterback Alex Smith completed 16 of 22 passes for 162 yards and two scores. He also ran for a touchdown.

Carr had a rough day, completing 31 of 48 passes for 283 yards and two touchdowns with three costly interceptions as the Raiders (5-7) took a huge blow to their wild-card chances.

"I played a lot of football in my life, won a lot of games lost a lot of games," said Raiders safety Charles Woodson, who forced a fumble and recovered two fumbles. "But today was probably one of the hardest losses I've been a part of in my career."

The Raiders trailed 26-20 and faced third-and-16 from their 16-yard line with under four minutes left. Carr's pass over the middle went off the fingertips of diving wide receiver Amari Cooper and deflected to Branch. Branch made a diving interception, got up and raced 38 yards to the end zone.

"Marcus was telling me to go down," said Branch, who kept the ball after his interception. "Nah, I got to live out my dreams."

The Chiefs went for two points, and Smith hit tight end Travis Kelce in end zone, making it 34-20.

The Chiefs opened the second half with an 80-yard scoring drive capped by running back Spencer Ware's 10-yard touchdown run up the middle, making it 14-14 with 9:16 left in the third quarter. Running back Charcandrick West's 18-yard burst and Smith's 26-yard pass to s Kelce set up Ware's score.

Oakland countered with an 86-yard drive as tight end Lee Smith caught his first touchdown pass of the season, a 5-yard throw from Carr on second-and-goal. Carr had thrown incomplete on third-and-6 from the 12, but Chiefs linebacker Derrick Johnson was penalized for roughing the passer, extending the drive.

Kicker Sebastian Janikowski missed the extra point, leaving the Raiders' lead at 20-14.

The Raiders appeared on their way to padding their lead, but on second-and-10 from Kansas City's 33, Carr was hit by two Chiefs as he threw, and the ball barely made it over the line of scrimmage, where Mauga intercepted. Mauga rumbled 65 yards to the Raiders' 2.

"Guys were just trying to make a play," Mauga said. "I just happened to be right there at the right spot and the ball just fell into my hands. The only thing in my mind was try to get as close to the goal line or even score. I was hoping I could score but I ran out of gas."

Carr was angry at himself for his costly mistakes.

"I'm pretty ticked off, especially on how some of them happened," Carr said. "I get pretty upset. Those things will happen. It just stinks that it happened all back to back like that."

Mauga's interception and return set up a 1-yard touchdown catch by Maclin in the right flat with 11:17 left to play. The Chiefs' PAT failed when holder Dustin Colquitt had trouble getting the ball down and Cairo Santos never attempted a kick.

The Chiefs quickly got the ball back when Peters intercepted a Carr pass and returned it 58 yards to the Oakland 13. After his interception, Peters ran to the stands and gave the ball to his mom.

"I truly appreciate they let my mom and family come in here with their red," Peters said. "We grew up as Raider fans and we love the silver and black, but now we love this red and gold. That was huge for me to be able to give my ball to my mom and get an interception at home."

Two plays later, Smith hit Maclin on a 13-yard touchdown pass, giving Kansas City a 26-20 lead. Cairo missed the point after, pushing it wide right.

Oakland drove into Chiefs territory but stalled at the 31, and Janikowski missed a 49-yard field goal attempt with 5:36 remaining, hitting the left upright.

"Tough way to finish," Raiders coach Jack Del Rio said. "Promising afternoon, lot of back and forth. It just got away from us. Turned the ball over and you can't do that. The last four drives were three turnovers and a missed field goal. That's not the way you want to close out a game you want to win."

NOTES: Chiefs starting DE Mike DeVito suffered a concussion. ... Chiefs starting LG Jeff Allen sustained a high ankle sprain. ...Raiders starting safety Nate Allen left the game with a knee injury. ... Chiefs OLB Dee Ford made his first career NFL start, replacing Justin Houston (knee),who was inactive. ... Raiders C Rodney Hudson, a former Chief, missed his second consecutive game due to a sprained right ankle. Tony Bergstrom started again in his place. ... Former Raiders WR Tim Brown received his Hall of Fame ring during a halftime ceremony.