The Mariners recovered an on-sides kick to open the game, but the MU defense forced a punt.
Williams turned a third-and-10 slant into an 81-yard gain to set up a first and goal.
After a short gain by Clayton Vleck, Leap hit Dieter on third down for the first score of the game and a 7-0 lead with 9:47 left in the first quarter.
USMMA responded with a 14-play, 80 yard drive to tie the score with 4:22 to go in the first period.
Leap and Dieter connected again on a 23-yard scoring strike to cap an 11-play, 75 yard drive to put MU ahead, 14-7, early in the second quarter.
After four straight USMMA scores, the Cougars answered with a seven-play, 71-yard scoring drive.
Klayton Kelly's 11-yard reception on third down moved to ball to the MU 47 yard line and Leap ran for 11 yards to the USMMA 37.
Vleck ran for five yards and another Kelly reception set up a first down at the 29 where Leap hit Dieter for their third scoring connection of the day to get within 35-21 with 3:54 left in the third period.
A 46-yard Leap to Williams connection on third-and-18 moved the Cougars to the USMMA 14 yard line. Leap and Mark Rainey combined for 13 yards on two carries before Leap scored from one yard out with 3:48 to play.
Kelly had three catches for 41 yards to set up Leap's four-yard TD run to get the Cougars within 49-35 with 3:54 remaining.
Tyler Collins led the MU defense with 13 tackles while Nick Yeager had 11 and Jerry Struble had 10 stops.
The Cougars will host Albright in their MAC opener, Saturday.
