Juan Fernandez chipped in 13 points for the Owls (3-1). Brooks and Allen dished out seven assists apiece and Fernandez had five, setting career best for all three players.
Craig Williams added 10 points off the bench for the Owls.
The Owls had an 11-2 run midway through the first half, taking take their first double-digit lead, 25-14, with just over 5 minutes remaining before halftime. They led by 10 points at the break.
Temple broke away for good early in the second half, using a 12-2 run to take a 54-34 lead with just under 9 minutes to play.
Jauwan Sciafe was the only Cardinals player to reach double figures, scoring 10. Jarrod Jones, who entered the game averaging 19 points per game, was held to nine points for Ball State (2-1).