Robinette, starting after senior Austyn Carta-Samuels had season-ending surgery to repair a torn ACL in his left knee, also had an 8-yard scoring run as Vanderbilt built a 24-0 lead in the first half.
After Houston (8-4) pulled even by scoring 24 points in the third quarter, Vanderbilt reclaimed the lead on Brian Kimbrow's 21-yard touchdown run in the fourth quarter.
Vanderbilt (9-4) closed the season with five straight wins, adding to third-year coach James Franklin's status as a possible candidate for coaching vacancies, including at Penn State and with the NFL Browns and Redskins. The Commodores played in three straight bowl games under Franklin - a first for the program - and completed their first back-to-back nine-win seasons.
Vandy players doused Franklin with a water bucket in the final seconds.