UCLA trailed by 10 points early in the game, but led by as many as six points in the first half after getting a spark off the bench from Bryce Alford and Zach LaVine.
The score was tied, 37-37, at the half, but a UCLA zone that bothered the Blue Devils in the first half didn't after that.
Duke improved to 9-2. UCLA fell to 9-2.
The Bruins' first loss came in their first test of the season, against Missouri earlier this month at Columbia.
David Wear led UCLA with 16 points.
Duke freshman Jabari Parker led all scorers with 23 points. Quinn Cook and Rodney Hood each had 14 points for the Blue Devils.