Houston trailed 13-3 at halftime but scored the next 14 points on a pair of long runs by quarterback D'Eriq King. His 33-yarder came on the final play of the third quarter and his 16-yarder gave the Cougars a 17-13 lead with 6:50 left.
Two plays later, Banks eluded pressure up the middle and heaved a pass to Encalade, who out-jumped a defender at the 15 and ran into the end zone.
Houston went for it on fourth-and-1 from Tulane's 32, but Luke Jackson broke up a pass attempt with 2:41 remaining in the game.
Encalade made eight catches for a career-high 186 yards. It was the 12th-most receiving yards in program history, trailing Ryan Grant's 187 in 2013. Encalade had 101 yards receiving in the first half.
Jonathan Banks had 68 yards on the ground and Dontrell Hilliard added 52 for Tulane (5-6, 3-4 American).
King was 18-of-26 passing for Houston (6-4, 4-3) with one interception.
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