Ahmad Walker added 16 points and 10 rebounds for Stony Brook (17-4, 8-0).
Trae Bell-Haynes led Vermont (13-10, 5-3) with 13 points and Ethan O'Day contributed 11 points and 10 rebounds.
The score was tied at 33 at halftime. Warney hit back-to-back jumpers out of the break to put the Seawolves up for the remainder of the game.
Warney's dunk at the 6:02 mark gave Stony Brook a 61-53 lead. But O'Day followed with a layup and Nate Rohrer hit a 3 to cut it to 61-58 with 3:37 left.
After a timeout, Carson Puriefoy buried a 3 and Warney's layup pushed the lead back to eight. The Catamounts shot just 1 for 7 from the field after the timeout.