Johnson caught a 61-yard touchdown pass from quarterback Conor Rhoda in the first quarter, and running back Shannon Brooks had a 1-yard touchdown plunge for Minnesota later in the first quarter.
But the Gophers couldn't pull away from the visiting Bulls until late in the fourth quarter.
Clinging to a 14-7 lead in the fourth quarter, the Gophers used a time-consuming, 13-play drive that was capped by Emmit Carpenter's 43-yard field goal with two minutes left.
Buffalo receiver Anthony Johnson caught 11 passes for 140 yards and a touchdown from Bulls' quarterback Tyree Jackson in the first quarter.
Fleck led Western Michigan to an undefeated regular season and a berth in the Cotton Bowl last year, before accepting the job at Minnesota.
He played two quarterbacks Thursday. Rhoda, a senior, started and completed 12 of 21 passes for 176 yards, with a touchdown and an interception.
Demry Croft, a sophomore, completed 7 of 11 passes for 63 yards and led the clinching fourth-quarter drive.
Tyler Johnson caught six passes for 141 yards, all coming in the first half.
Jackson completed 22 of 42 passes for 211 yards for Buffalo, with 16-yard touchdown to Anthony Johnson.
Minnesota rolled up 408 yards while Buffalo had 262.
The Gophers are picked to finish in the middle of the pack in the Big Ten West Division.
Minnesota travels to take on Oregon State next week.
Buffalo is picked to finish near the bottom of the MAC East Division. The Bulls are coming off a 2-10 season.