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KANSAS CITY, Mo. -- Up and down the sideline, the Kansas City Chiefs were telling each other the game wasn't over. Didn't matter that Philip Rivers was under center with less than a minute left, and that Nick Novak was poised to kick the winning field goal for San Diego.

The Chiefs have had their backs against the wall enough this season.

They certainly weren't going to just quit.

With first down at the Kansas City 15, Rivers called for the snap -- and the ball never got into his hands. It squirted loose on the field, bounced under a scrum, and finally emerged in the hands of Chiefs linebacker Andy Studebaker, who was running to the sideline in joy.

The game headed for overtime, and Ryan Succop eventually knocked through a 30-yard field goal to give the Chiefs a dramatic 23-20 victory over the Chargers on Monday night.

"Our guys were saying, 'It ain't over 'till it's over. Keep playing, and digging,' " Chiefs coach Todd Haley said. "You never know what will happen."

Kansas City (4-3) became the first team in NFL history to lose its first three games and share at least part of a division lead after four more. The Chiefs are also the first team since the Pittsburgh Steelers in 2000 to win four straight games after losing their first three.

Rivers could have prevented all of it from happening.

"I haven't had one in years," Rivers said of the fumbled snap. "It's unfortunate. I dropped it. This one is rough. You blow it on a play that never should have happened."

Kansas City had its own chance to win in regulation, but Matt Cassel overthrew his wide receiver in Chargers territory and Eric Weddle's second interception sent the game to overtime.

San Diego won the toss but failed to pick up a first down, and Cassel calmly led Kansas City down field. Succop's field goal with 5:16 remaining gave the Chiefs their fourth straight win and moved them into a tie with San Diego (4-3) and the idle Oakland Raiders (4-3) in the division.

"We were saying, 'Don't quit,' " Studebaker said. "You never quit, even if it looks ugly. If you quit every time something looks ugly, you miss an opportunity to do something special."

Boy, was this one ever ugly.

Rivers wound up throwing for 369 yards, but he also had two interceptions and one big fumble.

The teams combined for eight turnovers, matching the most in an NFL game this season. The Chargers were called for 12 penalties worth 105 yards in a gruesome game on Halloween night.

One that looked pretty in the end to Kansas City.

The Chiefs got off to an abysmal start this season, losing their first two games by a combined 89-10 score and then dropping their third game on the road, at San Diego. Along the way, the Chiefs lost Pro Bowl running back Jamaal Charles, safety Eric Berry and tight end Tony Moeaki for the season.

They started moving in the right direction against division doormats Minnesota and Indianapolis, and then romped to a 28-0 win over Oakland last week.

Now, they are tied for the lead in the AFC West.

"It's everybody," Haley said. "And I hate to mention one without mentioning them all, because everybody fought their tail ends off to make that result what it was."

The Chiefs had things going early, getting a 36-yard field goal from Succop in the first quarter and then capitalizing on Rivers' second interception in the first few minutes.

With the ball at the Chargers 39, Cassel dropped back to pass and saw Jonathan Baldwin streaking for the end zone. The wide receiver out-jumped fellow rookie Marcus Gilchrist for his first career touchdown catch, giving the Chiefs a 10-0 lead.

Novak kicked a field goal midway through the second quarter for San Diego, but he missed another late in the second quarter, and Succop hit one with just a few ticks on the clock for a 13-3 halftime lead.

The Chargers' defense kept them in the game in the third quarter, holding the Chiefs to two three-and-outs and picking off Cassel for the second time. Kansas City only managed 44 yards of offense in the second and third quarters combined.

Novak kicked three field goals in the third quarter, drawing the Chargers within 13-12, but their inability to get into the end zone cost them dearly.

Kansas City finally got its offense in gear, marching 74 yards in 10 plays early in the fourth quarter. Jackie Battle finished off the drive by leaping over the scrum from a yard out, giving the Chiefs a 20-12 lead with 12:01 left.

It sure didn't last long.

Rivers completed four straight passes covering 74 yards -- one for 27 yards to Vincent Jackson on third-and-13 -- before Curtis Brinkley leaped in from 2 yards out for the Chargers' first touchdown.

Going for the 2-point conversion and the tie, Rivers floated a pass to Brinkley in the flat and he was thrown back by cornerback Brandon Carr. The officials ruled that Brinkley nudged the ball over the goal line, though, and the decision was upheld by video review.

It was the fourth replay call that went against the Chiefs.

Rivers' butterfingers made that a moot point.

"They had no timeouts. We were in position to go kick the game-winning field goal," Chargers coach Norv Turner said. "It didn't happen. It looked to me like Philip got a little anxious and came out early. That's a very unusual way to not win a game."

Game notes

The Chargers signed LB Bront Bird from the practice squad and released WR Bryan Walters before the game. ... Chiefs S Jon McGraw left the game with a shoulder injury. ... San Diego CB Quentin Jammer left the game in the second half with cramps.