The Tigers grabbed an early 7-4 lead. However, Verona closed out the period with a 9-2 run keyed by Dalton Miller's 3-point play to lead 13-9.
Verona frustrated Exeter, collecting six steals in the second quarter and forcing the Tigers to turn the ball over 21 times in the contest.
The Wildcats outscored the Tigers 14-12 in the second period to lead 27-21 at halftime.
The Tigers tried to make a run in the third quarter and trimmed the Wildcats' lead to three points (30-27) with 4:15 left in the frame, but a Seth Losack layup gave Verona a 5-point cushion it would never relinquish.
Cody Musick sank a short jump shot as time expired to lift the Wildcats to a 40-33 lead after three quarters of play.
Verona opened the final period with an 8-0 run to erase any thoughts of an Exeter comeback and outscored the Tigers 13-8 in the quarter.
Exeter scoring leaders: Austin Johnson, 15 points; Kong Lee, 12; Blake Walker, 7; Colten Stringer, 4; Terry Cook, 2; and Ty Pendergraft, 1.
Verona scoring leaders: Losack, 17; Ascencion Estrada and Miller, 10 apiece; Tomas Estrada, 6; Brent Downs and Musick, 4 each; and Austin Dawson and Justin Smith, 2 each.
The Tigers host McAuley on Dec. 10. Tipoff is set for 6 p.m.