The Crimson Tide went into last month's SEC title game with hopes of a national championship, but those were wiped out by Florida, and Alabama finished with two straight losses and a 12-2 record.
Utah (13-0), champions of the Mountain West Conference, completed the season as the only major college football team in the country without a loss. They kept their unbeaten season going by scoring in the final minute to defeat TCU, which went on to hand Boise State its only setback of the season in their bowl game.
Utah took a 21-0 lead in the first 11 minutes and then regained the momentum after Alabama rallied within four points early in the second half.
Johnson first-period threw touchdown passes of 7 yards to Brent Casteel and 18 yards to Bradon Godfrey and Matt Asiata scored on a 2-yard run.
Alabama closed within 21-10 at halftime, thanks chiefly to a 73-yard punt return for a score by Javier Arenas, and then recovered a fumble early in the third quarter that led to a 4-yard touchdown pass from John Parker Wilson to Glen Coffee.
Utah regrouped, however, and drove 66 yards in seven plays. Johnson's third touchdown pass of the game -- a 28-yarder to David Reed -- gave the Utes a 28-17 advantage and Alabama could not recover.
Johnson completed 27-of-41 passes for 320 yards. Freddie Brown caught 119 yards worth of passes on 12 receptions.
Utah outgained Alabama 337 yards to 214.