Gill was shooting 63 percent from the line for the Cavaliers (27-6) but calmly made both free throws after James Robinson's hanging layup had brought the Panthers to within 49-48.
Pitt had a chance to tie with 4 seconds left, but Justin Anderson tipped Robinson's 3-pointer to Gill with 0.5 seconds left.
Joe Harris scored 12 points to lead the Cavaliers, who shot 47 percent against the fifth-seeded Panthers (25-9) to earn their first trip to the final since 1994.
The Cavaliers earned their first outright regular-season title since 1981 and only their second No. 1 seed. This was their first semifinal appearance since 1995, and they're now a win from their second tournament title -- the other coming in 1976.
Virginia will face the North Carolina State-Duke winner Sunday.
Lamar Patterson and Talib Zanna each scored 15 points to lead Pitt, which was in its first ACC tournament. The Panthers, who were going for their first appearance in a league tournament championship game since winning the Big East title in 2008, shot just 37 percent.
The teams met only once this year, with Malcom Brogdon hitting a 3-pointer with 0.4 seconds left in a 48-45 road win on Feb. 2. This one came down to another tight finish, though the Cavaliers kept the Panthers at arm's distance for most of the final minutes and maintained a fragile hold on the game.
After trailing by eight, Pitt closed to within 47-44 and got a good look for the tie on Josh Newkirk's 3-point attempt with 1:45 left, but never could level the game.
Robinson stripped Brogdon and drove for a layup over Akil Mitchell -- hitting it through contact from Mitchell but with no whistle -- to cut the deficit to 49-48 with 10 seconds left to set up Gill's big free throws.
Virginia led 26-24 at the break and used a strong shooting start to the second half to finally build a working margin. The Cavaliers took their biggest lead on Gill's hook shot to make it 45-37 with 9:30 left.
But the Cavaliers suddenly went cold, going 6 minutes without a point while the Panthers started inching back into the game.
Pitt opened its first ACC tournament with a 29-point romp against Wake Forest in Thursday's first round. The Panthers then dominated No. 15 North Carolina for much of Friday's quarterfinals, building a 20-point lead before having to hold off a frantic comeback attempt to reach the semifinals.
Pitt lasted the longest of the three new league members. Notre Dame was eliminated in the tournament's first-round opener on Wednesday, while N.C. State upset No. 11 Syracuse in Friday night's quarterfinals.