The Texans have scored 17 unanswered points to take the lead on the injury-depleted Titans.
Houston, which trailed 14-0, now leads 17-14 early in the fourth quarter.
Watson threw a 28-yard touchdown pass to DeAndre Hopkins with 58 seconds left in the first half.
Watson has completed 16 of 23 passes for 231 yards with two touchdowns and an interception. Fuller has seven catches for 112 yards and the score.
Blaine Gabbert has struggled, going 9-of-15 for 67 yards and a touchdown.