The Dragons trailed by 43-40 midway through the second half but went on a 16-6 run to pull away.
During the run, Gerald Colds converted a three-point play to cut the deficit to one. He drove the lane on Drexel's next possession, scored, and was fouled. He missed the free throw but grabbed the rebound and fed Givens for a layup that put Drexel ahead by three.
Another Givens layup gave Drexel a 56-49 lead with 2 minutes, 58 seconds to play.
Drexel, which is outrebounding opponents by more than 14 a game, won the battle of the boards, 36-22, and had 11 second-chance points against the Red Flash (2-9).
Colds added 17 points and Chris Fouch had 10 for the Dragons.
St. Francis was led by Anthony Ervin with 20 points. Chris Johnson and Mislav Jukic chipped in 10 points apiece for the Red Flash.
The double-double was Givens' fifth of the season.