Austin Chavis, Ben Cowles and Bobby Zmarzlak, among others, stepped up against Bryant.
The Terps racked up 11 hits and generated 11 walks.
While Dean issued five walks, he kept the Bulldogs off the board while on the mound.
Alleyne tied a program record with six hits while Zmarzlak hit two homers.
Cowles powered the Terps' offense past the Blue Hens with two extra-base hits — one being a homer.
After posting just five runs in three games against Coastal Carolina, the Terps were potent on Wednesday.
"We just gave them too much," Maryland coach Rob Vaughn said.