Ibrahima Thomas and Deonta Vaughn each added 10 points and Thomas had 11 rebounds for the Bearcats (15-9, 6-6 Big East), who won for the first time in three games, and kept their NCAA tournament hopes alive.
Kemba Walker had 14 points for the Huskies (14-11, 4-8), who were 3-4 while Calhoun was out with an undisclosed medical condition, and have lost five of their last six. Jerome Dyson added 13 points for UConn, which was held to its lowest point total since 2002.
Cincinnati outrebounded UConn 46-32 and had 19 offensive boards.
Calhoun received a standing ovation as he walked onto the XL Center court for pregame warmups, and another when he was introduced to the crowd. But those same fans booed the Huskies in the second half.
The Bearcats used a 19-3 run to turn a 22-17 first-half deficit into a 36-25 second-half lead.
Cincinnati stretched that to as many as 15 points, and when Dion Dixon hit a layup with 3:38 left it was 51-36.
UConn tried to mount a late comeback, and cut the deficit to six twice in the final 2 minutes.
But the Bearcats hit their free throws down the stretch and held on for the win.
Neither team shot well. Cincinnati hit 37 percent from the field, but held UConn to 34 percent. The Huskies made just nine of their 30 shots in the second half.
The 67-year-old Calhoun left the team on Jan. 19 at the end of a three-game losing streak. After associate head coach George Blaney took over, the team won two straight, including an upset of then-No. 1 Texas. But since that game, the Huskies are just 1-5.
It didn't take Calhoun long to get back into the job. The Hall of Famer made three substitutions in the first 2 minutes, and called a timeout less than 3 minutes in, after Cincinnati took a 4-0 lead.
The Huskies didn't score until Stanley Robinson hit a jumper almost 5 minutes into the game, but trailed just 9-7 at the first media timeout.
The Bearcats hit just four of their first 18 shots, and UConn went on a 7-0 run to take its first lead. A steal, drive and dunk by Robinson made it 20-14, but Cincinnati closed the first half on an 8-2 run to tie the game at 22.
Connecticut scored five points in the first 10 minutes of the second half.
UConn lost 71-69 at Cincinnati in December, the Big East opener for both schools, when the Huskies were ranked No. 10 in the nation.
The win was Cincinnati's second in eight road games.