Sheehan found a wide-open Marques Parks for a 9-yard touchdown pass to pull the Falcons within one, and coach Gregg Brandon went for two to end it. The winner was a tight throw near the sideline, caught by Barnes with three Gophers converging.
New Minnesota coach Tim Brewster saw his team rally from a 21-0 deficit midway through the third quarter. Amir Pinnix's 22-yard touchdown run gave the Gophers a 31-24 advantage on the first possession of the extra period.
Pinnix was the spark behind the comeback, rushing for 168 yards and two scores -- plus the tying touchdown catch with 8:53 left in regulation. Freshman quarterback Adam Weber had two costly first-half turnovers and an overall rough performance in his debut. He went 15-for-31 for 188 yards and two touchdowns.
Sheehan, a sophomore, was good enough early to help the Falcons establish the big lead and clutch enough late to lift Bowling Green's record against the Big Ten to 5-12 since 1972. The Falcons beat Purdue that year when Don Nehlen was the head coach.
Brandon's first season was 2003, when the Falcons defeated Purdue and Northwestern and lost by a touchdown at Ohio State after Urban Meyer left for Utah.
Though the Falcons returned 17 starters, they went 4-8 last season and were predicted by media covering the Mid-American Conference to finish fifth in the league's seven-team East Division.
The Gophers scored on four straight possessions to take their first lead. Jason Giannini's 33-yard field goal with 2:12 left came too soon, though, because Sheehan marched the Falcons close enough for a 35-yard kick by Sinisa Vrvilo that tied the game with 3 seconds left.
Bowling Green intercepted Weber's desperation heave to end regulation, nearly returning it in Cal-Stanford-band-on-the-field fashion until a tackle by Eric Decker at the Minnesota 30.
Weber struggled in offensive coordinator Mike Dunbar's "Spread Coast" system in the first half, and the Gophers went back to basics after halftime behind their big offensive line.
Pinnix's 4-yard score with 6:10 left in the third quarter was followed by another clock-draining drive that closed on a 13-yard screen pass from Weber to Ernie Wheelwright that pulled the Gophers within 21-14 on the first play of the fourth quarter.
After a near-perfect first half, the Falcons faded behind dropped passes, penalties and stalled drives. Vrvilo missed a 42-yard field goal between Minnesota's second and third touchdowns.
But they did their damage in the first half.
Minnesota's weakness under previous coach Glen Mason was usually defense, and the Gophers were as soft as ever in the first half against a spread scheme similar to what they face in practice every day.
Sheehan threw for 174 yards in the first quarter alone, frequently using the middle of the field in sets with four and sometimes five receivers. Backup quarterback Anthony Turner subbed in and surged up the middle for 7 yards to reach the end zone and give the Falcons a three-touchdown lead with 2 1/2 minutes remaining before the half.
Brewster's energy helped the Gophers boost their season-ticket base, and the crowd was announced at 49,253 -- almost as big as the Michigan game last season. The actual number of attendees, however, was certainly several thousand less.