Lamar Patterson added 18 points, seven assists and four rebounds for the Panthers (13-9, 2-7 Big East), who never trailed while improving to 12-0 against Top 10 teams at the Petersen Events Center.
Otto Porter led the Hoyas (16-4, 6-3) with 14 points and Henry Sims added 10 but Georgetown couldn't overcome a 17-point first-half deficit.
The Hoyas pulled within 55-49 with 4:09 remaining before Patterson fed Dante Taylor for a dunk and then hit Robinson for a wide-open layup to give the Panthers some breathing room.
When Ashton Gibbs hit a pull-up to push the lead to 61-49, the Panthers were on their way to a second straight win following a miserable eight-game losing streak.
The program's longest skid in more than a decade ended with a relatively easy victory over struggling Providence on Wednesday. Coach Jamie Dixon tried not to make too much of the win, calling it simply a starting point for the long climb back.
If beating the Friars was one small step, knocking off the Hoyas was a good-sized leap.
The return of point guard Tray Woodall from injury has given the Panthers a sense of identity they've lacked this season. Pitt struggled offensively without their only proven ballhandler. Though he wasn't as sharp as he was in his second game back against Providence — when he scored 17 points and made all four of his 3-pointers — he didn't have to be.
Woodall finished with just four points but added a game-high 10 assists while leading an offense that had little trouble sharing the ball. Pittsburgh finished with 20 assists on 25 field goals, picking apart Georgetown's defense with relative ease.
Pitt took control with arguably its best 10 minutes of the season, using a 15-1 run midway through the first half to go in 29-12. While the Panthers surged behind Robinson and Talib Zanna, the Hoyas went ice cold while missing 10 straight shots and three of four free throws during the stretch. Georgetown couldn't hold onto the ball either, giving it away four times during Pitt's run, not all of the miscues coming due to pressure.
Jason Clark ended the 7-minute field goal drought with a pull-up jumper and the Hoyas used a pair of late 3-pointers to get within 33-22 at halftime.
Georgetown's momentum carried over after the break. The Hoyas drew within 39-34 on a three-point play by Clark. Yet the Panthers, perhaps buoyed by the first truly raucous atmosphere at The Pete all season, responded.
Robinson, bothered by lingering soreness from offseason knee surgery, hit consecutive layups, the second off a nifty feed from Patterson.
Patterson added a 19-footer to again give the Panthers some space.
The Hoyas, who had their three-game winning streak snapped, struggled to get into a consistent rhythm. Though they forced the Panthers into 17 turnovers, they couldn't turn the giveaways into points.
Pitt has abandoned its traditional man-to-man defense this season, going with a zone that helps it overcome a significant size disadvantage in the frontcourt. The Panthers held their own against the Hoyas, limiting Georgetown to 42 percent shooting and holding a 35-23 advantage on the boards.
It added up to Pitt's biggest win of the season, as the Big East's winningest program over the last decade continued an upswing it hopes will carry into the second half of its conference schedule.