Since starting the season 14-0 and finding its way into the Top 25, first-year coach Donnie Jones and UCF have struggled.
Those tough times continued on Saturday night in Houston as the Owls (9-10, 1-4) knocked down free throws in the final minute to clinch a 57-50 victory over the Knights.
UCF (14-4, 1-4) shot just 32 percent in the first half, but still found itself up 27-25 at the break.
However, they would be unable to hold onto that lead after halftime as Rice used a 15-1 run to open up a 40-28 lead following a Tamir Jackson lay-up with 12:18 remaining.
The Knights battled back to knot the game at 43 when Marcus Jordan sunk a pair of free throws 5:26 to play.
Tamir Jackson hit the first of two free throws to give Rice the lead right back with just under five minutes to go and the Owls would not trail again.
TAlthough they didn't trail, it was still a one-point contest with 28 seconds to play when UCF's A.J. Rompza was whistled for a technical foul for reaching across the baseline when Rice was throwing the ball in.
Connor Frizzelle, who scored a team-high 15 points, converted the two free throw attempts and Tamir Jackson hit two more a second later to open up a 55-50 lead with 27.2 left.
Arsalan Kazemi posted a double-double for the Owls, as he finished with 11 points and 14 boards.
UCF was led by Keith Clanton, who tallied 18 points and grabbed eight rebounds. Marcus Jordan scored ten and was the only other Knight to reach double figures.
Both teams shot below 35 percent for the contest and UCF was just above 30. Each club was 20-of-28 from the charity stripe.