Hines tied the score with 36-yard touchdown run in the third quarter and Gillislee hauled in the winning TD pass on a 45-yard play in the fourth quarter to give Florida (8-1, 7-1 SEC) the win in its conference season finale.
Missouri (4-5, 1-5) crossed into Gator territory six times in the second half but failed to score and wound up with its third loss in four games.
The Tigers racked up 327 net yards to 272 for Florida, but the Gators picked off four of James Franklin's passes and sacked him twice.
Franklin finished 24-of-51 for 236 yards and a Kendial Lawrence scored on a 1-yard TD run in the second quarter.
Jeff Driskel was 12-of-23 for 106 yards for Florida. Gillislee carried 16 times for 68 yards.