Omar Jacobs threw five scoring passes for Bowling Green, the fourth of which was a 17-yarder to Sanders with 37 seconds left in the first half that gave the Falcons a 35-28 lead at the break.
Bowling Green then dominated the second half with Pope catching a 14-yard touchdown pass from Jacobs and then producing his second one-yard scoring run of the contest.
The game was played in a cold rain.
Jacobs hit Sharon with touchdown throws of 18 and 36 yards in the first half and also threw a 31-yarder to Sanders that made it 28-14.
Jacobs completed 28 of 35 passes for 360 yards while Danny Wimprine of Memphis was 26 of 39 for 325 yards and four touchdowns.
Bowling Green completed the season at 10-3 while Memphis was 8-5.