KANSAS CITY, Mo. -- This was the Kansas City Chiefs' seventh win in as many tries in a season full of surprises, but their locker room celebration was a little longer and a little louder after Sunday’s game against the Houston Texans.

The Chiefs were at last impressed with what they accomplished in beating the Texans 17-16 at Arrowhead Stadium. For the first time this season, the Chiefs took an opponent’s best shot, albeit an opponent struggling with injuries and having a season as disappointing as Kansas City’s is satisfying.

But the Chiefs survived, and after the Denver Broncos' loss Sunday night, sit alone atop the AFC West. The Texans played about as well as they reasonably could have, considering they started the game without injured quarterback Matt Schaub and finished it without, among others, running back Arian Foster and linebacker Brian Cushing.

The Chiefs won the fourth quarter of a tight game yet again, breaking through to sack Houston quarterback Case Keenum four times and making him fumble in the final two minutes to kill the Texans' final possession.

“Some games are going to get messy and some games are going to be hard," free safety Kendrick Lewis said. “It’s the NFL. However it comes, however we need to get it, we all pull together and get the win."

It wasn’t pretty and, in many quarters, the one-point victory against the short-handed and 2-5 Texans will further talk that the 7-0 Chiefs are the products of their lousy schedule. They have just one victory over a team that has a winning record, that being last month’s one-point home win against the Dallas Cowboys, now 4-3.

That may eventually prove to be true. After games the next two weeks against the Cleveland Browns and Buffalo Bills, the Chiefs’ schedule takes a decidedly more difficult turn. Five of the final seven games are against the Denver Broncos, San Diego Chargers and Indianapolis Colts.

Just don’t try selling that notion to the Chiefs. They’ve made a habit of strangling their opponent in the fourth period, and it’s to the point where they believe they’ll make that happen each week. Overheard in the celebration as the team entered the locker room were the words of one player: “This is how we do it."

This was indeed how the 2013 Chiefs do it, how after finishing a league-worst 2-14 last season they are 7-0 this year. Though neither team scored in the final 15 minutes, the Chiefs owned the fourth quarter against the Texans.

Houston took 13 snaps in the period, not counting punts. The Texans’ fourth-quarter offensive output: negative-1 yard. Seven plays went for zero or negative yards.

The Chiefs have outscored opponents 57-17 in the fourth quarter, a pace they may not be able to continue. Linebacker Tamba Hali, who had 2.5 sacks in the final period, including the one that made Keenum fumble, looked as weary as if he’d played all seven fourth quarters on Sunday.

“It’s definitely draining doing it this way," he finally said. “You put so much into the game. After the game you want to be happy about it. But we’ve got another tough game coming up against Cleveland."

It’s easy to think now, after the fact, that there should have been a sense of inevitability about the fourth quarter. But so much was different about the first three periods Sunday that no one could have taken anything for granted about what would happen next.

The Chiefs’ pass rush had been meek for most of the first three quarters. Kansas City afforded plenty of time to Keenum, enough for him to complete six passes of more than 25 yards. Making his first NFL start and taking his first regular-season NFL snap, Keenum for three quarters played better than the Texans had a right to hope.

The Chiefs, who had been living off turnovers with an NFL-best differential of plus-12, for the first time this season coughed up the ball more than their opponent. The only turnover that mattered was Houston’s only one of the day, the Keenum fumble on what would be the Texans’ last snap of the game.

“You counter [turnovers] with some big plays," Chiefs coach Andy Reid said. “You counter with good defense."

The Chiefs seem to have an endless supply of those two elements, at least in the fourth quarter. They had five sacks and two interceptions in the final period last week against the Oakland Raiders, two interceptions in the fourth quarter the previous week against the Tennessee Titans.

Nine of Kansas City's 16 defensive takeaways occurred in the fourth quarter, when the Chiefs are at their best.

“We love to make plays when the game is on the line," Hali said. “Our guys are playing with a lot of confidence. We believe we’ll be the ones making those plays every week."