Marcus Jordan contributed 11 points for UCF (20-8, 9-5 Conference USA), which improved to 15-1 at home this season.
John Bohannon was the only player in double figures for UTEP (14-14, 7-7) with 16 points.
UCF led 52-45 before getting back-to-back three-point plays from Sykes and Clanton that ignited an 11-0 game-ending run.
The Knights were up 25-23 at halftime, despite shooting only 29.6 percent (8 of 27) from the field. Sykes was the only UCF player to make more than one shot in the half.
The junior forward and his team heated up in the second half, when he scored 18 points, and better ball movement allowed UCF to end UTEP's four-game win streak.