Smith compiled 240 aerial yards with an interception and was backed by a strong defensive effort produced a Chiefs' record five sacks of Houston quarterback Case Keenum.
Jamaal Charles led the Kansas City ground game, picking up 86 yards with a touchdown on 21 carries.
Keenum, filling in for the injured Matt Schaub, managed to make good on 15-of-25 pass attempts with no interceptions, but committed a key fumble on a sack by Tamba Hali with less then 2 minutes left to kill any chance of driving for a late game-winning score.
Running back Arian Foster and linebacker Brian Cushing each left the game with injuries for the Texans (2-5).
Dennis Rodman pledges to end trips to North Korea
Interpol investigating stolen passports on missing flight