Jelan Kendrick provided a spark for the Runnin' Rebels (5-4), coming off the bench to score 18 points. He had 11 at halftime by hitting all three of his field goals and all four free throws.
Birch broke a tie with a three-point play at the 5:08 mark of the first half to send the Rebels on their way. Kendrick's shot at the buzzer made it 45-35.
Javonte Green led Radford (7-4) with 18 points.
Christian Wood, who had 10 points off the bench, had a three-point play with 8:57 left in the game to put UNLV up 70-45. The Rebels shot 52.5 percent and went 13 of 19 at the foul line, where Radford was 4-8.