Kansas City, Mo. ? The Kansas City Chiefs’ offense finally proved it could win a game.

Their defense finally let them down.

After driving for a go-ahead touchdown in the waning minutes against San Diego on Sunday, Alex Smith the rest of the offense could only watch as Philip Rivers answered with a 26-yard pass to Seyi Ajirotutu with 24 seconds left that gave the Chargers a dramatic 41-38 victory.

It was the most points the Chiefs had scored this season. Also the most they’d allowed.

“I mean, yeah, when we scored, we put the pressure back on them,” said Smith, who threw for 292 yards and three touchdowns.

“They’d been good on offense all day, and Philip was playing good, so yeah, there was a chance. But we knew we’d put the pressure back on them.”

Rivers was unflappable, though, against a Chiefs defense missing top pass rushers Tamba Hali and Justin Houston. He took advantage of time in the pocket to shred the Kansas City secondary, and then hit the most unlikely of his wide receivers with the pass that decided the game.

“It was a great throw,” Chiefs coach Andy Reid said. “It’s a game of inches and we were off by an inch on coverage. We had a man over top and a man underneath and they put it right on the spot.”

The touchdown, and the eighth lead change, deflated a raucous Arrowhead Stadium.

Smith had calmly guided Kansas City (9-2) downfield just moments earlier, completing five of six passes on the drive. His throw into tight coverage to Dwayne Bowe with 1:22 left gave the Chiefs a 38-34 lead, and put the game in the hands of a defense that had been among the NFL’s best.

Just not on this day. And not against this quarterback.

Rivers wound up throwing for 392 yards and three touchdowns for San Diego (5-6), which ended a three-game losing streak. Danny Woodhead had touchdowns rushing and receiving as he picked up the slack for Chargers running back Ryan Mathews, who left with a hamstring injury.

Ladarius Green had a 60-yard touchdown reception in the fourth quarter, while Keenan Allen had nine catches for 124 yards against a porous Chiefs defensive backfield.

“It’s one of those you’ll never forget, that’s for sure,” Rivers said. “It’s kind of what our season’s been about. Can you drive and score at the end in 2 minutes?”

San Diego finished with 491 yards of offense against a Chiefs defense that had allowed more than 17 points just once: last week’s 27-17 defeat in Denver.

One of the big reasons for that was its inability to get pressure on Rivers after Hali and Houston left in the second quarter. Hali had a sprained right ankle and Houston a sprained left elbow, and both of them are due for MRI exams on Monday.

“It’s tough, the way those guys dominate and get pressure,” Chiefs cornerback Brandon Flowers said.

“But at the end of the day, us as a unit, we’ve got to get better. No excuses, man, no excuses. San Diego came out and played. They executed. They were moving the ball at will, it seemed like today. So we’ve got to go back to the drawing board and improve what we do.”

Especially with the return game against the Broncos looming next week.

While there will be plenty on the line in the AFC West, there’s little chance it will be as entertaining as the back-and-forth nail-biter the Chiefs played on Sunday.

San Diego pulled ahead 17-14 when a 54-yard pass to Eddie Royal set up a 1-yard TD run by Mathews, but the Chiefs took it back on Jamaal Charles’ second touchdown run. The Chargers answered with a TD run by Woodhead, only for Anthony Fasano to pull in a touchdown catch for Kansas City.

Green’s first career touchdown gave San Diego the lead back with 7:50 left, and while the Chiefs had one more answer left, so did the Chargers.

“That’s what the game’s all about,” Chargers coach Mike McCoy said. “When the game’s on the line, who’s going to come up and make the big play? Who’s going to make the big stop?”

Notes: The Chargers have won 10 of their past 12 against Kansas City. … The Chargers’ Antonio Gates three catches for 21 yards, making him the fourth TE in NFL history with 700 catches and 9,000 yards. … Smith dropped to 0-3 against San Diego as a starting QB. … Chargers CB Shareece Wright left briefly with an undisclosed injury but returned to the game. .. The Chiefs played without starting RG Jon Asamoah (calf, shoulder) and RT Eric Fisher (shoulder).