After Washington's touchdown, the Titans held the Texans to a punt and were going to try to run out the clock, but Ahmard Hall fumbled to give Houston the ball back at the Tennessee 36.
With the No. 3 seed in the AFC already locked up and perhaps not wanting to risk an injury in overtime, the Texans went for a two-point conversion.
But Texans tight end Joel Dreessen was whistled for a false start on the first attempt and the snap sailed over Delhomme's head on the second, with Tennessee recovering for the win.
Matt Hasselbeck threw for 297 yards and two scores on 22-of-35 passing for Tennessee (9-7), which kept its slim playoff chances alive with two straight wins to end the regular season.
The New York Jets lost on Sunday, but Tennessee still needs wins by Oakland and Denver and a loss by Cincinnati to make the playoffs.
T.J. Yates started at quarterback for Houston, but left the game in the first quarter with an injury. Yates completed all four pass attempts for 47 yards in his lone drive. Delhomme replaced him and completed 18-of-28 passes for 211 yards and a touchdown.