It was a dominant defensive performance by the Chiefs, who took advantage of five Brian Hoyer turnovers.
The Texans quarterback put forth one of the ugliest playoff performances in recent memory, going 15-of-34 for 136 yards with no TDs, four picks, and a lost fumble.
The Chiefs scored at the first possible opportunity when return man Knile Davis took the opening kickoff back for a 106-yard touchdown. Despite the hot start, the offense was unable to break the game open early, taking a 13-0 lead into the half before Chris Conley caught a 9-yard touchdown pass late in the third quarter.
The receiving touchdown came at exactly the right time for the Chiefs, as wide receiver Jeremy Maclin left the game shortly before with, what appeared to be, a significant knee injury. Maclin's status for the Chiefs' divisional-round game will be a major talking point going forward.
The Chiefs' last playoff win also came in Houston, when Joe Montana led a Marty Schottenheimer-coached team to a 28-20 victory over the Houston Oilers.
Kansas City will now face one of the AFC's elite teams as the Chiefs will travel to Denver or Foxborough next week to battle the Broncos or Patriots. If the Pittsburgh Steelers beat the Cincinnati Bengals, K.C. faces the Broncos; if the Bengals win, it will be Chiefs-Patriots at Gillette Stadium with a trip to the AFC Championship Game on the line.