Storm Johnson added 127 yards rushing for UCF (7-1, 4-0), which has the inside track to the league's automatic BCS bid, with victories against the Cougars and Louisville.
The Cougars drove to the UCF 10 in the final minute, but came up empty on back-to-back passes from John O'Korn into the end zone. The first went off star receiver Deontay Greenberry's finger tips and second to Aaron Johnson was then broken up by UCF linebacker Brandon Alexander.
O'Korn had a touchdown pass and two interceptions for the Cougars (7-2, 4-1).
The Knights had three giveaways and lost receiver Breshad Perriman to a targeting hit early in the fourth quarter, but rallied to preserve the win.
Trailing 13-7 in the fourth, Houston pinned UCF on its own 2, but the Knights got some space on a 17-yard completion from Blake Bortles to Perriman.
Bortles went to Perriman again two plays later, but his pass over the middle was broken up by Cougars' cornerback Zach McMillian. McMillian was flagged for targeting on the play, and was ejected after a review.
Perriman remained down on the field for several minutes receiving medical attention and was carted off.
The Knights weren't shaken, though, and Stanback scored his second touchdown of the game five plays later to stretch UCF's lead to 19-7 with 10:23 to play. The seven-play, 98-yard drive was the Knights' longest of the season.
Following a UCF missed field goal, Houston got life when O'Korn found Wayne Beadle in the end zone from 12 yards out to close the gap to 19-14.
UCF then gave the Cougars the ball right back with 3:02 to play after going three-and-out.
Houston went to the air and moved quickly, eventually using a 14-yard pass on third down by O'Korn to get into the red zone. But UCF held - and held on to sole possession of first place.
After defense-dominated first half, offense began to pick up in the final 30 minutes.
Houston's first possession of the second half ended abruptly when Alexander intercepted a deflected pass by O'Korn.
But the Knights turned it right back over when Bortles fumbled after being sacked from behind.
The Cougars worked quickly and needed just four plays to set up a 24-yard touchdown run by O'Korn to put them up 7-6.
The Knights offense recovered, and capped a 10-play, 75-yard drive with a 15-yard touchdown run by Stanback to make it 13-7.
UCF took a 6-0 halftime lead into halftime, but could have had a much larger cushion if not for some costly turnovers.
The first quarter ended without points for Houston, ending a streak of 39 straight quarters with points.