SAN DIEGO (AP) Alex Smith, Travis Kelce and the rest of the Kansas City Chiefs have goals far bigger than simply winning the AFC West.

The Chiefs finished off their domination of the division when they beat the last-place Chargers 37-27 Sunday in possibly the final NFL game in San Diego.

''Right now it's awesome that we won it and we're happy that we achieved that goal, but everything is kind of moving forward and we've got our eyes set on the biggest prize yet, and that's getting a Super Bowl win,'' said Kelce, the star tight end. ''There's no doubt in my mind that we can go get that thing.''

The Chiefs haven't been to the Super Bowl since beating Minnesota following the 1969 season.

San Diego fired coach Mike McCoy after the game.

Smith threw for two touchdowns and ran for another for the Chiefs (12-4), who clinched the division with the win and Oakland's loss at Denver.

Smith, who went to nearby Helix High in La Mesa, scored on a 5-yard scramble early in the second quarter to tie the game at 10. He threw a 4-yard touchdown pass to wide-open Charcandrick West later in the quarter to put the Chiefs ahead for good. That followed the first of two interceptions of Philip Rivers that led to 10 points for the Chiefs.

''For us it was such a big swing, to go from potentially playing a road game in the wild card to a bye and hosting a game,'' Smith said. ''There was no in-between there. We took care of our end and got some help from Denver, so it was pretty sweet.

''We saw the score there at the end, and we had our deal sealed up. Pretty awesome, and to win the division is special as well, that's something that this group hasn't done.

''It's crazy to sweep the division,'' he said of going 6-0.

Smith was intercepted once, on a deflected pass that Jahleel Addae returned 90 yards for a touchdown to pull the Chargers (5-11) to 20-17 in the third quarter. Smith came right back and threw a 2-yard scoring pass to West, who again was wide open.

Rookie Tyreek Hill showed some fancy footwork in returning a punt 95 yards for a touchdown in the final minute of the third quarter.

MCCOY FIRED

McCoy was 27-37 in four seasons, with the Chargers having lost 23 of their last 32 games. They've also lost 13 of their last 14 AFC West games dating to late in the 2014 season. He had one year left on his contract.

THE LA OPTION

For the second straight year, the Chargers were playing perhaps their final game in San Diego.

Last year, Chairman Dean Spanos was in the process of trying to move the team to Carson to share a stadium with the rival Raiders. That plan was defeated by fellow NFL owners in January, but Spanos was given the option to move to LA if he couldn't come up with a way to replace aging Qualcomm Stadium. A Nov. 8 ballot measure asking for $1 billion in increased hotel occupancy taxes to help fund a new downtown stadium was overwhelmingly voted down.

Spanos has until Jan. 15 to announce whether he'll move the team

The Rolling Stones' ''The Last Time'' played on the PA during a break in the action after a Chiefs field goal made it 37-20 late in the game.

Smith, for one, hopes that doesn't happen. He grew up in the San Diego area and played at Qualcomm Stadium in high school championship games and in college when Utah visited San Diego State.

''For me growing up here, I think it'd be tragic if there wasn't a team here. If there wasn't football in this town, it would be weird for me.''

GATESY

Chargers tight end Antonio Gates tied Tony Gonzalez for the most touchdown catches in NFL history by a tight end with 111.

Gates tied the mark on a 2-yard toss from Rivers early in the second quarter to give the Chargers a 10-3 lead. Gates caught the ball and extended it in his right hand to break the plane.

The Chargers tried to get Gates sole possession of the record in the fourth quarter but couldn't.

''They were not going to let him get that touchdown,'' Rivers said. ''I was looking at him every other time, too. We did the best we could.''

Late in the game, Rivers threw a 12-yard TD pass to San Diego's other tight end, wide-open rookie Hunter Henry.

RIVERS PICKOFFS

Rivers was intercepted twice to set a career high with 21. Rivers' previous high was 20 in 2011.

''We gave ourselves a chance. We turned it over twice. which killed us,'' Rivers said.

INJURIES: Chiefs S Eric Berry left with an ankle injury in the second half. Chargers S Darrell Stuckey left with a knee injury, LB Christopher Landrum suffered a concussion and G Orlando Franklin had a shoulder injury.

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