Kasey Wilson added 11 for the Knights (11-15, 3-12 American Conference), who outscored Rutgers 9-2 in the last 2:38 of the game to win for only the second time in their last 13 games.
Rutgers led 35-26 at the half and held UCF without a field goal during a six-minute stretch in the middle of the second half to push the lead to 54-39 on a follow shot from Greg Lewis with 9:28 left in the game.
UCF responded with an 11-0 run that included a pair of 3-pointers from Spurlock. His last bomb cut the deficit to 54-50 with six minutes left.
The Knights pulled within 63-62 when Sykes converted a fastbreak layup, but missed the free throw attempt that would have made it a 3-point play and tied the game. He made up for it on the next possession, driving right through the middle of the Rutgers' defense for a layup that put UCF ahead 64-63 with 41 seconds to play.
Calvin Newell added two free throws and Spurlock had one more to make it 67-63 with nine seconds to go.
Etou made a meaningless layup in the final second.
The Knights were out-rebounded 44-32 and only shot 38.9 percent but scored 19 points from the foul line on 30 attempts while Rutgers was just 5 of 10. However, the Scarlet Knights also had 18 turnovers and had three players foul out.