The Bears' win finished off a long night of basketball at AT&T Stadium, the home of the Dallas Cowboys and the host venue for this season's Final Four.
Both the men's and women's teams from Kentucky and Baylor took part in a double header that attracted only a small crowd due to the ice-covered roads in the Dallas-Fort Worth area.
In addition, the women's game that opened the action went four overtimes before Kentucky defeated Baylor 133-130 in a battle of unbeatens. It was the highest scoring Division I women's game in NCAA history.
That marathon delayed the start of the men's game by 90 minutes.
Kentucky (7-2) overcame a slow start in the men's game and built a nine-point lead early in the second half.
Baylor then rallied into the lead and eventually held the Wildcats to just two points over the final three minutes.
Cherry's jumper put Baylor (8-1) in front by four and free throws down the stretch from Brady Heslip and Royce O'Neale protected the lead.
Cherry led Baylor with 18 points while Cory Jefferson and Isaiah Austin had 13 each. Julius Randle led Kentucky with 16 points.