It was the 11th double-double this season for the 7-foot-3 junior, who also had six blocks.
Jerome Dyson led UConn (22-1) with 19 points and Jeff Adrien had nine points and 14 rebounds. Adrien's final rebound, on the last shot of the game, gave him 1,000 for his career, just the sixth player in school history to score 1,000 points and grab 1,000 rebounds.
Stu Douglas hit six 3-pointers and scored 20 points to lead Michigan (15-9), which was coming off a 71-51 victory Thursday over Penn State. Manny Harris added 15 for the Wolverines.
Connecticut, playing its first week as the No. 1 team since 2005-06, hasn't lost since dropping a 74-63 decision to Georgetown in the Big East opener on Dec. 29.
UConn opened the game on an 8-1 run, punctuated by an ally-oop from A.J. Price to Stanley Robinson. But the Wolverines fought back using several back-door cuts to beat UConn's half-court trap and full-court press.
The Wolverines forced 10 first-half turnovers from the Huskies and went on a 9-0 run that turned a 21-20 deficit into a 29-21 lead.
The Huskies closed the half on a 12-5 run to cut the Michigan lead to 34-33. It was just the fifth time UConn has trailed at halftime this season.
The Huskies trailed 43-39 before scoring the next nine points take the lead for good.
Michigan never made it easy, though, holding UConn without a field goal for over four minutes late in the game. A layup by Dyson ended the drought and made it 61-53 with 2 minutes left.
Douglas hit two 3 pointers down the stretch, but UConn was able to answer from the free throw line and hold on for the win.
The Huskies came in 11-0 against non-conference opponents, and have won 14 consecutive home games against opponents outside the Big East since a 77-73 loss to Indiana on Jan. 20, 2007.
Michigan, which beat Duke and UCLA earlier in the year, has lost six of its last eight and heads home to face No. 13 Michigan State on Tuesday.
Calhoun is 5-1 against Beilein, who lost three times to the Huskies while he was with West Virginia, and once while at Richmond.
This was just the second meeting between the two schools, with Michigan winning the other 62-45 in 1939. The two school's will play again in the 2010-11 season in Ann Arbor.