Brian Cushing picked off an Alex Smith pass with 6:34 left in the opening quarter.
The Chiefs were in Texans territory, with a 2nd-and-5 at the Houston 28. Kareem Jackson tipped the pass, which was intended for Jeremy Maclin, and Cushing came down with the carom.
It was the first postseason interception of Cushing's career, and the fourth Texans' playoffs' interception in franchise history.
Two plays before that, Eric Berry intercepted a Brian Hoyer pass intended for Nate Washington.
Cushing also had a pair of tackles in the opening quarter.
The Texans trailed the Chiefs, 7-0.