Lamar Patterson added 12 points, seven assists and five rebounds for the Panthers (7-1), who overwhelmed the Titans (2-4) in the second half.
Ray McCallum led Detroit (2-4) with 24 points but the Titans shot just 32 percent (9 of 28) in the final 20 minutes to drop their third straight.
Detroit dominated for most of the first half, leading by as much as 13, but could do little when McCallum cooled off. The junior scored just five points after halftime as Pitt extended its defense to try and knock him off rhythm.
The Panthers had no such issues. Zanna and freshman point guard James Robinson combined for 14 points during a 16-3 burst midway through the second half that helped Pitt avoid the upset.
It was a significant step forward for the Panthers, who have struggled at times this season when Woodall isn't creating. Yet they did some of their best work with their senior captain either on the bench or taking on a secondary role.
Woodall did give Pitt its first lead of the second half with a 3-pointer that put the Panthers up 42-41. The teams traded baskets for the next couple of minutes before Robinson put Pitt ahead for good on a runner that made it 51-49 with 7:40 to play.
Zanna added two free throws then followed with a dunk off an assist from Patterson before Robinson hit a step-back jumper to make it 57-49. Detroit's Nick Minnerath stopped the surge with a jumper of his own, but it hardly mattered. Robinson knocked down a 3-pointer on Pitt's next trip and Zanna ended the run with a tough layup in traffic to send the Panthers into their annual meeting with crosstown rival Duquesne on Wednesday riding a three-game winning streak.
The Titans are no mid-major pushover. The defending Horizon League champions have one of the best guards in the country in McCallum and were hardly intimidated by the venue. Detroit came in winless in its two previous games against power conference schools, but both were competitive losses to St. John's and Miami (Fla.)
McCallum and company were more than just competitive in one of the tougher places to play in the country. McCallum airballed his first shot, but quickly heated up no matter who the Panthers put on him. Robinson -- Pitt's best defender -- got the first crack, but McCallum kept calmly draining 3-pointers as Detroit went on a 20-4 surge to take command.
The Panthers have struggled against zones during the season's first month and looked lost after the Titans switched out of man-to-man early. Only Woodall seemed interested in being aggressive, and he kept Pitt close until picking up his third foul with 1:29 to go before the half when he bumped into McCallum as Detroit took a 37-29 lead at the break.
It wouldn't hold up, however, as Pitt put together perhaps its most complete half of the season against a quality opponent.
Follow Will Graves at www.twitter.com/WillGravesAP