Jabari Parker scored 23 points, while Rodney Hood and Rasheed Sulaimon added 11 points each for the Blue Devils (20-5, 9-3 Atlantic Coast Conference).
Wells had all 17 of his points in the second half for Maryland (14-12, 6-7).
Parker gave Duke the lead for good when his one-handed dunk over Damonte Dodd made it 68-67 with about 1:15 remaining.
Wells missed a jumper over Hood with about 50 seconds left. Duke milked the shot clock before Amile Jefferson missed a jumper that failed to draw iron, giving the Terrapins the ball.
The teams traded timeouts with 18.8 seconds left before Maryland worked the ball inside to Mitchell. He had one hook shot blocked by Parker with about 7 seconds left, and another tantalizingly bounced twice on the rim but would not fall through.
Jefferson grabbed the rebound, was fouled with 1.1 seconds left and hit a free throw to end the scoring.
Wells couldn't get off an 80-foot heave before the buzzer, sealing Duke's 30th straight victory at Cameron.
Duke missed 17 of its first 19 shots in the second half before Jefferson banked one in to tie it at 54 with 6½ minutes left. That came about 2 minutes after Wells capped a 12-1 run with a layup that gave the Terrapins their first lead at 54-52, and it was a one-possession game the rest of the way.
Duke were unable to take advantage of Maryland's drought early in the half, instead matching the Terps missed shot for missed shot. Maryland went 5 minutes between buckets early in the second half.
Duke finished at 33 percent from the field while Maryland shot 41.9 percent.