Andy Reid preached all week for the Kansas City Chiefs to rediscover their identity, to find the swagger that had gone missing during a three-game losing streak that put their playoff hopes in peril.

They found it during a five-minute stretch of the second half Sunday.

Their offense finally humming and their defense taking advantage of turnovers, the Chiefs scored three touchdowns in quick succession, propelling them to a 31-13 victory over the Oakland Raiders.

"It was kind of the focus all week of us kind of cutting it loose, going out there and playing for each other," said Alex Smith, who threw for 297 yards and two scores.

The Chiefs (8-6) were clinging to a 10-6 lead early in the third quarter against the same team that started their skid last month. But after Knile Davis scored a touchdown to cap a 70-yard drive, the Chiefs recovered a fumble, scored again then added one more touchdown to put away the game.

"Going into halftime, there were so many things we were so close on," Reid said. "The guys settled down."

Just about the only downside for Kansas City was the big shot that Jamaal Charles took on a carry near the goal line. He went through concussion testing on the sideline and was cleared to return later in the game. But he was eventually pulled with the outcome decided.

Derek Carr was 27 of 56 for 222 yards, throwing a TD pass in the final minute. But he also was sacked four times and fumbled a snap that led to a Kansas city touchdown.

The Chiefs, who had been poor against the run the past three weeks, even managed to bottle up Raiders running back Latavius Murray. The second-year pro had 112 yards and two scores on just four carries in their first meeting but was held to 59 yards on 12 carries Sunday.

"Their athletes made more plays than we did," the Raiders' Justin Tuck said. "Pretty much it."

The Raiders (2-12) have lost 10 straight on the road and still have not won back-to-back games since Weeks 7 and 8 of the 2012 season. That includes a pair of duds in the Show-Me State — they were routed 52-0 at St. Louis two weeks ago.

"You can't just blame one area," Carr said. "This is a team thing."

Both teams got off to slow starts in a penalty-filled matchup, but Kansas City finally got a jolt of energy when De'Anthony Thomas fielded a punt at his 19-yard line. Picking up a nice block from Kelcie McCray, the rookie somersaulted over the goal line for an 81-yard touchdown return.

"It's to the point where I'm starting to get a feel of it," Thomas said.

Chiefs kicker Cairo Santos atoned for missing his first field-goal attempt since Week 2 early in the second quarter by knocking through a 41-yarder. The Raiders' Sebastian Janikowski matched him with a 53-yarder as time expired to close within 10-3 at the break.

Oakland had a chance to make the game interesting in the third quarter when Travis Kelce fumbled and C.J. Wilson recovered. But in a fitting summation of the Raiders' season, Wilson ended up hurt on the play, and the Raiders went nowhere before Janikowski kicked another field goal.

The Chiefs took advantage of the opening — and a roughing-the-passer penalty on Justin Tuck — to go 70 yards on their next possession. Davis finished it off with a short touchdown run.

Carr fumbled the snap on the next play, Kansas City recovered and Smith hit Kelce from 20 yards for a touchdown. The Chiefs then forced a three-and-out, and Smith's 70-yard throw to Davis a moment later capped their three-TD spurt and gave Kansas City a 31-6 advantage.

"The whole second half, it started falling apart," said the Raiders' Charles Woodson, "and we were never able to recover and it got out of hand."