The Big Red (2-1) trailed 7-2 early but outscored the Blue Hens 13-5 to lead for the first time on Miles Asafo-Adjei's 3 with 10:34 to play in the first half.
Delaware (0-2) quickly regained the lead, 16-15, on Kaleb Clyburn's jumper and went up 18-17 with 7:13 to go until halftime. Cornell then took over with a 12-5 run. Groebe's layup started the spurt and put the Big Red up for good, 19-18, with 6:56 left in the first half.
Delaware had a better shooting mark than Cornell at 45.3 percent (24 of 53) compared to 42.6 percent (26 of 61), but committed 15 turnovers.
Anthony Gatlin scored 12 points on 3-of-3 3-point shooting for Cornell, which made 42.1 percent from long range (8 of 19).