Maine led 14-0 early in the second quarter before Hood scored from 2-yards out. Hood then capped off a 7-play, 83-yard drive with a 1-yard run to help the Black Bears take a 28-0 lead.
Hood finished with 102 yards on 14 carries. It was the first time since 2008 that Maine had two players rush for 100 yards.
Maine's defense held Bryant to just 186 yards on 59 plays (3.2 yards per play) and forced two turnovers in the win, including Khari Al-Mateen's 77-yard interception return for a touchdown.
The two squads played each other for the first time last season, with Maine coming away with a 28-13 victory.
Jordan Brown led Bryant with 63 yards rushing.