Sean Johnson led Duquesne (4-3) with 19 points but the Dukes struggled against the bigger, stronger, deeper Panthers.
Pitt outrebounded the Dukes 39-15 to offset 23 turnovers. The Panthers never trailed over the game's final 30 minutes but struggled putting Duquesne away.
Each time the Dukes drew close, Gibbs would answer with a big shot, including consecutive 3-pointers during a 14-6 run midway through the second half that gave Pitt some needed breathing room.
Taylor had missed the previous two games with migraine headaches and lost his starting job to freshman Khem Birch. Yet he made up for lost time, making all six of his shots from the field and adding 11 rebounds, playing so well Birch spent most of the second half on the bench.
The Dukes hoped to overcome their distinct size disadvantage by pushing the tempo against a Pitt team that has lacked the defensive tenacity that's become the hallmark of the program under coach Jamie Dixon.
It worked, for a couple of minutes anyway.
Duquesne's first three baskets were layups as the Dukes had little trouble beating the Panthers down the court, breathing life into a record Consol Energy Center crowd that appeared to have more Duquesne red in the stands than Pitt gold.
The Panthers took control with an 8-0 run early in the first half and slowly extended it to 38-27 at the break, with Zanna's dunk at the horn a perfect example of Pitt's dominance around the rim.
Woodall finished with nine points and seven assists but also gave it away six times. Gibbs had four turnovers, but made up for it with clutch shooting.
Duquesne kept making mini-surges at the Panthers, getting as close as 50-46 on a jumper by Mamadou Datt with just over 13 minutes to go.
Robinson sandwiched two layups around two 3-pointers by Gibbs and Taylor followed with a tip-in and then a dunk to extend Pitt's lead to 64-52. The Dukes got back within 64-57 on a tip-in by Kadeem Pantophlet but Patterson responded with a wide-open 3 to quell Duquesne's last best shot.
The Dukes had hoped to make a statement by knocking off the Panthers for the first time since 2000. There have been some near misses recently, including a double-overtime loss two years ago.
Coach Ron Everhart stressed his team would have to be competitive on the backboards to win, a problem for a team that starts three guards and had been getting out-rebounded by 10 a game coming in.
Things got worse against the Panthers. Duquesne shot a respectable 52 percent from the field but managed just three offensive rebounds as Pitt's frontline swallowed up missed shots with ease forcing the Dukes to try and hang in on turnovers.
Pitt did its best to help, but ended up winning its fourth straight heading into Saturday's rematch with Tennessee, which beat the Panthers a year ago.