Burke was 12 of 17 from the field and had seven rebounds for the Bruins (17-10, 10-5 Pac-12), who won for the eighth time in the last nine games. Japreece Dean added 14 points and Michael Onyenwere had 12.
UCLA outscored the Ducks 36-14 over a large portion of the second half to lead 68-60. Oregon pulled to within 70-69 on Sabrina Ionescu's 3-pointer with 34 seconds left, but the Bruins scored the last four points at the foul line.
Erin Boley led the Ducks (24-3, 13-2) with 20 points, Ionescu had 18 and Maite Cazorla 13.