Shabazz Napier scored 23 points, including a big 3-pointer with a minute left, and Roscoe Smith added 14 points and seven rebounds for the Huskies (18-12, 8-10 Big East) who kept alive hopes for an at-large bid to defend their NCAA national championship.
J.J. Moore led Pittsburgh (16-15, 5-13) with 16 points.
The Panthers, who were coming off a 20-point win over St. John's, came back from a 14-point halftime deficit to take a 61-60 lead with 2:51 left, but could not hold on and lost for the sixth time in seven games.
Pittsburgh, which trailed by 14 at the half, took its first lead of the game at 61-60 on a 3-pointer by Tray Woodall.
But UConn went on an 8-1 run, going up 66-61 on Napier's 3-pointer with just over a minute left, right after Smith took a charge from Moore to get UConn the ball.
A 3-pointer on the other end by Gibbs cut the lead to five with 31 seconds left. But the Huskies hit their foul shots.
Connecticut seemed inspired by their coach's return and jumped on Pittsburgh early, opening a 14-point halftime lead.
Calhoun spent much of the first half on the bench, occasionally pacing the sidelines or taking issue with the referees.
But by the time Pitt had cut the deficit to five with just over 11 minutes left, the Hall of Fame coach was back on his feet, his tie loosened, screaming encouragement and yelling when the Huskies failed to get out to defend the 3-point line.
A jump shot by Gibbs made it 48-45 with 10 minutes left and a 3-point play by Moore tied the game at 48 with 9:20 left. UConn went back up by six, before Moore tied it again with a jumper with 4 minutes left.
The Huskies closed the first half on a 15-4 run, scoring 12 points off nine Pittsburgh turnovers, to turn a 21-18 lead into a 36-22 halftime advantage after a 3-pointer by Shabazz Napier.
Pitt shot 63 percent from the field in the second half after being held to 31 percent before intermission.
This was the first time the two schools have met without either of them being ranked in 15 years.
Connecticut needed the win to improve its NCAA tournament resume. The Huskies had lost nine of their past 12 games and had won just five times since Jan. 1. But the Huskies came in with an RPI ranking of 36, and played what many experts said was the toughest schedule in the nation.
Calhoun received a standing ovation when he walked on the floor and another rousing ovation as he was introduced to the crowd.
The Hall of Fame Coach took his medical leave on Feb. 3 and missed the Huskies' last eight games because of the effects of spinal stenosis, a narrowing of the spine, normally associated with aging and sometimes with arthritis.
He underwent a two-hour surgery Monday in New York involved removing a large disk fragment that had been pressing on a spinal nerve. The surgeons decompressed the area around the nerve.
The team went 3-5 in Calhoun's absence, and is 5-6 this season without the Hall of Fame head coach this season. He missed the team's first three conference games while serving an NCAA suspension.
Calhoun now has 871 career wins, in sixth place on the career list and just five wins behind Adolph Rupp.
Pitt had won four of the last five meetings with Connecticut, but the teams had not played since last year's 76-74 win by UConn in the Big East tournament.
The two teams have combined for 12 Big East regular season or tournament championships over the past decade.