The homecoming game was supposed to be played Saturday but was postponed because of heavy rain and lightning.
Woodson made it 7-0 with a 13-yard pass to Kobie Booker in the opening quarter. Morgan's 1-yard run in the second period gave the Zips (4-3, 3-0 Mid-Atlantic Conference) a 14-0 lead.
Two field goals by Josh Grant sandwiched a 50-yard TD pass from Jon Wassink to D'Wayne Eskridge that got the Broncos within a point in the fourth quarter. Eskridge had seven catches for 93 yards.
Western Michigan (4-3, 2-1) had the ball with 45 seconds left but could only get to the Akron 39 before Wassink was sacked on the final play of the game.
Jarvi Franklin had 130 yards rushing for the Broncos.