Delaware's Eric Carter hit a jumper to retake the lead 72-71 with 58 seconds left in the second extra period and followed with two free throws with 18 seconds remaining.
Ryan Allen, who finished with a career-high 30 points, made two free throws in the final seven seconds to seal the win as the Blue Hens (16-11, 8-6 Colonial Athletic Association) won their third double-overtime game this season.
The teams scored three points apiece in the first overtime. Allen had three free throws and Howard split a pair of free throws and had a layup.
Carter finished with 16 points and Horton added 15.
Fobbs totaled 29 points with nine rebounds for Towson (9-17, 5-8). Tobias added 15 points and Dennis Tunstall pulled down 21 rebounds.