The Explorers, who led by 15 in the first half, fell behind by a point five times in the second.
Down 57-56 with 6:01 remaining, La Salle used a 9-3 run, with Zack scoring seven points, to lead by five with 2:59 left.
The Blue Hens could get no closer than three the rest of the way.
The Explorers hit 8 of 8 free throws in the final 53 seconds, finishing 23 of 25 from the line to make up for shooting 36.5 percent from the field (23 of 63). Delaware shot 45.2 percent (28 of 62).
La Salle’s Jerrell Wright finished with 14 points and 10 rebounds.
Delaware’s Jarvis Threatt scored 17 points and Devon Saddler scored 14. Jamelle Hagins added 12 points and 14 rebounds.