Adam Vinatieri also had three field goals for the Colts, who didn't commit a turnover.
"That's what coach [Chuck] Pagano has preached since I've been with the club," Luck said. "Limit turnovers on offense and create turnovers on defense."
Early on, the Chiefs appeared as if they were going to pick up right where they left off last week, when they hung 56 points on the Raiders. They marched downfield on the opening drive, and Charles took a carry around the right side 31 yards for a touchdown.
The Colts' defense stiffened after that, though, and the closest Kansas City came to scoring again in the first half came when Ryan Succop yanked a 47-yard field goal wide left.
"It was a team effort in not a very good way," Chiefs coach Andy Reid said. "You can't pull your foot off the accelerator when you get out that quick."
Meanwhile, Indianapolis kept taking advantage of breakdowns in the Kansas City pass defense, the most glaring one coming after running back Knile Davis fumbled in the second quarter.
Brown leaked out of the backfield unnoticed by the Kansas City defense, Luck hit him with a dump-off pass that he took virtually untouched 33 yards for a score.
"I think they busted the coverage," Brown said, "so that made my job a lot easier."
Brown's job wasn't a whole lot tougher when the Colts got the ball back in the third quarter off Smith's interception. He raced through a gaping hole, then tight-rope walked down the sideline 51 yards for a score — a video review showed that he somehow stayed inbounds.
Vinatieri added to the Colts' cushion with his third field goal, capping a drive kept alive by a defensive hold and a taunting penalty after the Chiefs had already held on third down.