Givens, a 6-foot-5 senior from Academy of the New Church, joined Bob Stephens and Malik Rose as the only Drexel players to record 1,000 points and 1,000 rebounds in a career. Givens did it on his second offensive rebound on a possession in which he went to the line and sank two free throws with 8 minutes, 18 seconds to play in the game.
Chris Fouch added 14 points and Frantz Massenat 13 for the Dragons.
Drexel took control of the game with an 11-1 run in the opening 5 1/2 minutes of the second half, holding James Madison (11-19, 4-13) without a basket for 5:32.
The Dragons shot just 36.0 percent from the field in the first half and watched the Dukes knock down seven three-point baskets in 11 attempts but only trailed by 35-34 at intermission. But they got back into their rhythm at both ends of the floor from the first whistle of the second half.
Drexel scored two baskets in the initial minute of the second half, an inside bucket by Givens and a three-pointer by Derrick Thomas, to take the lead for good. Givens had two more baskets in the 11-1 run, including a layup that gave Drexel a 45-36 lead with 14:48 to play.
Thomas later contributed a three-pointer and a dunk off a JMU turnover to give the Dragons their largest lead to that point, a 54-42 advantage with 11:26 remaining.
The Dukes scored seven straight points after that on two inside buckets by Gene Swindle and a three-point hoop by A.J. Davis to close to within 54-49 at the 9:27 mark. But Aquil Younger, on for foul-troubled Massenat, drained a three, and Givens hit two free throws to get the margin back to 10.
After a JMU basket, Massenat returned to knock down a trey to give Drexel a 62-51 lead with 7:12 to play, and the visitors never got closer than 10 the rest of the way.