The Panthers came up with school bowl record rushing and receiving performances from James Conner and Tyler Boyd as well as a strong relief appearance in the second half by redshirt freshman quarterback Chad Voytik.
Mid-American Conference champion Bowling Green hung in, however, and tied the game with 4:42 to go on a 15-yard pass from Matt Johnson to Ryan Burbrink.
Voytik then led the Panthers 52 yards in six plays to the game-winning field goal for the fourth lead change of the contest.
There will be 11 Atlantic Coast Conference teams in action during the bowl season, most of any league in the country, and Pittsburgh was the first of those to see action. The Panthers finished the season with a 7-6 record after winding up next-to-last in the ACC's Coastal Division.
Connor gained 229 yards on 26 carries and scored Pittsburgh's first touchdown of the game in the opening quarter. He broke the school bowl rushing record of 202 yards set by Pro Football Hall of Fame member Tony Dorsett in the 1977 Sugar Bowl.
Boyd caught eight passes for 173 yards, most ever for the Panthers in a bowl game, and his 63-yard reception set up a Pittsburgh touchdown early in the fourth period that broke a 20-20 tie.
Voytik came on to open the second half after starter Tom Savage suffered a rib injury shortly before intermission. Voytik was good on 5-of-9 passes for 108 yards and scored in the fourth quarter on a 5-yard run at the end of a 98-yard drive.
Bowling Green (10-4) captured the MAC title by downing previously unbeaten Northern Illinois in the league's championship game.
Johnson completed 20-of-32 passes for 272 yards and two touchdowns for the Falcons.
Pittsburgh outgained Bowling Green 488 yards to 292.