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.
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Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.