Josey's game-winning score came with 3:34 remaining and clinched the SEC East title for the Tigers (11-1, 7-1 SEC).
They now go on to face the Auburn Tigers for the conference crown. Auburn clinched the SEC West with an upset over top-ranked Alabama Sunday in their annual Iron Bowl game.
Josey finished with 96 yards on 13 carries.
James Franklin completed 18-of-28 passes for 233 yards with a pair of TD tosses, also providing 80 rushing yards on 18 tries.
Johnny Manziel went 24-of-35 passing for 195 yards with a TD for the Aggies (8-4, 4-4).