The Blue Devils trailed 61-56 with 2:15 to go but Quinn Cook's 3-pointer 17 seconds later drew Duke to within two points.
Plumlee later grabbed an offensive rebound of Cook's missed jumper and was fouled by Ryan Anderson with 47 seconds to go, hitting both free throws to put Duke ahead for good.
He added another foul shot with 25 seconds left and the Blue Devils (21-2, 8-2 ACC) held on for their fifth straight win.
Plumlee finished with 19 points and 11 rebounds while Seth Curry added 18 for Duke.
The Eagles (10-13, 2-8) were paced by Olivier Hanlan with 20 points.