Belmont went up 25-14 thanks to a 13-2 run in the first half. The Bruins' spacing and ball movement led to 19 assists and plenty of open looks, but Kentucky's size always posed a problem.
Craig Bradshaw led Belmont with 22 points. Drew Windler had 21 points while going 5-of-8 from 3-point range, but only one came in the second half.
"With this lineup in particular, we pretty much have to make 3s in any game," Byrd said.
The Bruins struggled with foul trouble in the second half. Evan Bradds fouled out with 1:56 to play after scoring 12 points on 5-of-5 shooting, and Reece Chamberlain fouled out in the game's closing seconds.
Three more Belmont players finished with four fouls.
What pleased Kentucky coach John Calipari most about the victory was how his players overcame adversity. The Wildcats haven't always done that, most recently during last week's loss at North Carolina in which they let a game within their reach slip away.
Against the Bruins, they not only had to seize control but maintain it.
"We fought like heck," Calipari said. "It's a hard team to play. They're going to shoot 30 3s. If they're making them, you lose.
"Against Carolina they made (15). Carolina lost. And they make 14 against us, we probably lose. ...We guarded it well enough and kind of got into their legs a little bit."