The Bruins led throughout, building leads as big as 13 points in the first half. Drexel charged back in the early stages of the second period with five consecutive points by Damion Lee getting the Dragons within 44-40 with 17 minutes to play.
UCLA pulled away slightly but next couldn't shake the Dragons. Drexel got within one point -- the last time at 66-65 on Franz Massenat's shot with 2:21 -- to go before Adams made a pair of free throws.
Tony Parker followed with a dunk off a pass from Norman Powell. Lee had a final basket for Drexel with 57 seconds left but Adams added two free throws with 3 seconds to go to provide the final margin.
Adams' team-high point total came on just 4-of-12 shooting but he was 7-of-8 from the free-throw line. David Wear and Zach LaVine each had 14 points for the Bruins who also got 12 points and 12 rebounds from Kyle Anderson.
Massenat ended with a game-high 20 points and Lee had 17 for Drexel.