Three straight plays went nowhere and the Texans had to settle for a field goal.
It was a virtuoso display by the NFL's stingiest defense, and a signature stand in a stellar second half.
The Chiefs kept repelling the Houston offense the rest of the way, and the result was a 17-16 victory to extend their perfect start.
"You know as well as I do you win with great defenses. That's how it rolls," Chiefs coach Andy Reid said. "You can't be successful like we are without a great defense."
"It was a physical game," Charles said, "the kind of a game this team needs to go far."
The game was still in doubt even after the Chiefs' goal-line stand. They had to punt with 1:46 left, but the Texans had no timeouts. Case Keenum threw an incompletion on first down, and then was stripped by linebacker Tamba Hali on the ensuing play.
Derrick Johnson recovered the ball for the Chiefs, and Smith simply kneeled on it from there to run time out. The result was a 7-0 start for Kansas City, trailing only the 9-0 mark put up by the 2003 team for the best in franchise history.
In the Super Bowl era, 31 teams have started 7-0 and all qualified for the playoffs. Fifteen of those 31 clubs advanced to the Super Bowl and nine have won it.
"It's confidence," said Hali, who was part of the Chiefs' two-win team last season. "Guys believe in what we're doing. They believe in one another, and that goes a long way."
Keenum, making his first NFL start in place of the injured Matt Schaub, threw for 271 yards and a touchdown for the Texans.
His performance was overshadowed by a pair of crushing injuries: Running back Arian Foster left in the first quarter with a hamstring injury and did not return, and linebacker Brian Cushing was carted off with a left knee injury in the second half.
"It was very detrimental to us," said Texans coach Gary Kubiak, whose banged-up team is riding its first five-game skid since Nov. 6-Dec. 11, 2005.
"When they can pin their ears back, they're very, very difficult," Kubiak said. "They came and got us pretty good there late in the game."
The Texans moved the ball well early on, taking the lead on Randy Bullock's 48-yard field goal. But the scoring drive proved costly when Foster left for the locker room, and then emerged a short while later in a gray sweatsuit.
"I'm going do everything I can to get healthy and come back and fight," he said afterward.
The Chiefs took the lead later in the first quarter when Charles pounded into the end zone from a yard out to cap an 82-yard drive. But the Texans, behind Keenum's unflappable play, retook the lead on a 29-yard touchdown pass to DeAndre Hopkins.
"He did a great job," Kubiak said of his young quarterback, who beat out T.J. Yates for the starting nod. "He's got some things he's got to understand when they come after him. But he made some great football plays to get his team in position to win."
Indeed, the Texans still led 10-7 midway through the second quarter. Smith proceeded to guide the Chiefs 97 yards in 15 plays, and his 5-yard draw gave the Chiefs the lead at halftime.
Bullock tacked on two more field goals for Houston, and Ryan Succop hit one for the Chiefs, who came within inches of extending their 17-16 lead early in the fourth quarter.
Tight end Anthony Fasano caught a pass at the goal line and was ruled down, and Reid was unsuccessfully in challenging that it should be a touchdown. Charles was stuffed on the next play, and Smith's pass to wide open Sean McGrath on fourth down was out of bounds.
It turned out that the missed points didn't matter.
The Chiefs' defense made sure of that.
The Chiefs had five sacks, giving them 36 on the season. ... Ben Tate had 50 yards rushing for Houston. ... The Texans did not commit a turnover until Keenum was stripped at the end. They had an AFC-leading 15 turnovers coming into the game. ... Smith had 231 yards passing.