Undercuffler connected with Green for a 15-yard score and a 7-0 lead for the Great Danes (6-4, 4-2 Colonial Athletic Association) after one quarter.
The Blue Hens (4-6, 2-4) answered with Nolan Henderson's 4-yard TD toss to Jourdan Townsend to knot the score at 7 at the 9:32 mark of the second quarter. But Albany responded, using just three plays to go 75 yards for a score. Undercuffler's pass to Green covered the final 64 yards.
Delaware pulled even on Will Knight's 28-yard TD run and took a 17-14 lead into halftime when Jake Roth booted a 21-yard field goal on the final play.
After a scoreless third quarter, Undercuffler directed a 10-play, 73-yard drive that culminated with his 13-yard TD toss to Jerah Reeves for a 21-17 lead. Delaware punted twice and turned the ball over on downs from there.
Undercuffler completed 13 of 23 passes for 176 yards, while Green finished with seven catches for 132 yards. Karl Mofor led the Great Danes' ground attack with 132 yards on 22 carries.
Henderson was 8-of-17 passing for 141 yards. Knight ran for 79 yards on 14 carries and caught two passes for 61 yards.