Jourdan Townsend gave Delaware (6-1) a 7-0 lead on the Blue Hens' first possession with a 17-yard touchdown run on his only carry of the game. Henderson needed just four plays on the Blue Hens' next drive to connect with Yarns for a 14-0 lead in the nonconference matchup.
Morgan State (2-5) closed to within 14-7 at halftime on Alfonzo Graham's 2-yard touchdown run with 1:23 left in the second quarter.
Henderson's 7-yard touchdown run was the only score of the third quarter, pushing Delaware's advantage to 21-7.
The Blue Hens added three scores in the final period - Khory Spruill's 2-yard touchdown run, a 39-yard field goal by Andrew MacMillan and backup quarterback Ryan O'Connor's 7-yard TD toss to Brett Buckman.
Henderson completed 13 of 29 passes for 206 yards with one interception for Delaware.
Graham carried 20 times for 83 of the Bears' 99 yards on the ground. Carson Baker completed 4 of 8 passes for 35 yards, while Duce Taylor threw three interceptions - completing 6 of 11 passes for 24 yards.
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