Smith went 27 for 45 passing for 312 yards and gained 46 yards on the ground for the Golden Hurricane (10-4), who closed out their season with six straight wins.
Tarrion Adams threw a touchdown pass and rushed for 112 yards and a score for Tulsa, which had lost five of its last seven bowl games.
Tyler Sheehan completed 14 of 19 passes for 141 yards while Roger Williams got the only score on a kickoff return for the Falcons (8-5), who had a four-game winning streak broken.
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