Blair added a game-high 10 rebounds and Keith Benjamin had 11 points for the Panthers (20-8, 8-7 Big East), who won their 20th game for the seventh consecutive season.
The game featured seven ties and seven lead changes and neither team opened up a lead of more than seven. The game was tied at halftime, and Cincinnati (13-14, 8-7) opened the second half on an 11-4 run, but Pitt scored the next seven points to tie it again at 40.
Pitt held a two-point lead late until Levance Fields' 3-pointer with 54 seconds left made it a two-possession game.
The win was the first for Pitt since starting point guard Fields returned from injury.
The Panthers started the season 11-0, but Fields injured his foot during a loss to Dayton on Dec. 29 after Pitt had climbed to No. 6. The team went 8-4 without Fields and lost all three games since he returned Feb. 15 at Marquette.
Fields had seven points and a team-high five assists.
Jamie Dixon became the first Pitt coach to win 20 games five seasons in a row with a victory that strengthens the team's chances of making the NCAA tournament for the seventh straight year.