UCF (16-12, 9-5) has beat Rice (3-24, 0-14) in five of the last six meetings. The Knights have won four of their last five games.
UCF squandered a 19-point, second-half lead, allowing the Owls to get within 58-56 on a pair of free throws by Patrick Britton with 2:30 remaining. Rice, however, could get no closer as the Knights hit 7 of 8 free throws in the final 2:20 to seal the victory.
Taylor led UCF with 20 points. Noel finished with 19 points and four rebounds. UCF committed 19 turnovers, but out-rebounded Rice, 38-26.
Lawrence Ghoram led Rice, which hasn't won since beating Texas State in December with 23 points.
Rodney Foster scored 15 points and pulled down five rebounds for the Owls.
UCF committed 12 first-half turnovers, but Rice couldn't capitalize. The Owls shot only 31 percent from the floor in the first 20 minutes, including 0 for 9 from three-point range. The Knights used a 19-3 run to take a 29-13 lead. UCF led 39-23 at halftime.