The young Wildcats (7-2) had a 50-41 lead when Julius Randle, one of three Kentucky freshmen playing in their home state, had a slam dunk with 13 minutes left.
Baylor (8-1) responded with a 15-5 run in which Chery, the junior college transfer who is now the Bears' point guard, came up big. His two free throws with 6 minutes left put the Bears up 56-55 and they never trailed again.
Randle had 16 points for Kentucky while Aaron Harrison had 15 and James Young 14 with four 3-pointers.
Isaiah Austin and Cory Jefferson had 13 points each for the Bears, who beat Kentucky for the second straight year. Rico Gathers had 13 rebounds.
Blue-clad Kentucky fans easily outnumbered those of the local team in what they certainly hope isn't their only trip to the Dallas Cowboys' massive stadium this season. It will be much fuller in four months.
With Baylor's football team playing at home about 100 miles away Saturday with a chance to clinch the Big 12 title, and icy conditions that made driving treacherous from the Waco campus, the crowd was under 10,000.
Plus, the game already scheduled to start after 9 p.m. local time started more than an hour after that. The Top 10-ranked women's teams from the two schools played four overtimes in the opener of the doubleheader. No. 5 Kentucky beat No. 9 Baylor 133-130 in the highest-scoring Division I women's game ever.
It was the third straight season the Baylor and Kentucky men played. Last December, the Bears won 64-55 at Rupp Arena to end a 54-game home winning streak by Kentucky, which beat Baylor in an NCAA tournament regional final in March 2012.
Kentucky trailed by nine points early, but recovered to tie the game at 27, 29, 31, 33 and 35 before Andrew Harrison's 3-pointer with 19 seconds left in the first half put the Wildcats up 38-35. They opened the second half with an 8-2 run.
Baylor had a 16-7 lead after Jefferson had a rebound that led to his assist on Chery's jumper only 4:22 into the game.
The Wildcats responded with a 15-7 run, and were down by only one after Aaron Harrison's third 3-pointer in less than 5 minutes.
Young's 3-pointer with 7 minutes left tied the game at 27. That was the first time Kentucky hadn't trailed since Young scored its first five points of the game for a 5-4 lead.
Randle is from the Dallas area. The other Kentucky freshmen playing in their home state were 6-foot-6 twins Andrew and Aaron Harrison from Richmond, about 4 1/2 hours south, near Houston.