It was the Parks and Button show early on, as the pair joined forces for 20 of the team's first 22 points in the opening 13 minutes of the contest.
Button put the Cougars on the board first with a jumper before UCF scored the next seven points to take an early 7-2 lead.
Button and Parks then combined for nine of the next 11 points, as Park connected on the first of four 3-pointers to cap an 11-0 run as Houston claimed a 13-7 lead.
With Houston holding an 18-10 advantage, the Knights (12-15, 7-8) put together a 9-1 run over a three-minute span to tie the contest at 19-19 before Parks snapped the skid with another long-range bomb.
Parks' 3-pointer would start an 8-1 run for the Cougars to push Houston back out to a six-point advantage, but the Knights managed to cut the deficit back to three points at the break.
UCF took its first lead of the second half at the 12:38 mark and it appeared the tables were turning as the Knights pushed out to a 3-point advantage while the Cougars struggled with a half-court trap.
The Knights' defense temporarily stymied the Cougars and effectively limited Button on the offensive end, but the rest of the squad stepped up as Button continued to find open teammates.
Parks began a defining 16-5 Houston run with a jumper off an assist from Button, who then found an open Voché Martin under the basket as the Cougars reclaimed the lead.
On the next trip down, Button dished to a wide-open Parks, who buried her third 3-pointer of the game to give Houston a four-point advantage.
The Knights were able to cut the lead back down to one but couldn't get any closer, as Martin grabbed an offensive board and converted the put-back attempt and Parks rattled off her fourth bucket from downtown to kick the lead back to six points with 8:56 remaining.
Martin struck again with a jumper from the baseline and the Cougar defense limited UCF to just one field goal for a six-minute stretch as Houston built a double-digit advantage.
Parks put the icing on the cake with a long jumper with just under two minutes remaining and Button fittingly knocked down the final Houston bucket with 17 seconds remaining to seal the upset.
Parks, a Houston native, tallied 24 points off an 8-of-14 effort from the field, including four treys on six attempts, and a perfect 4-of-4 performance from the charity stripe.
In her final game in Hofheinz, Button posted 15 points to go with a career-high eight assists and four steals in 40 minutes of action. The 15 points marked the 24th time this season that Button managed to score in double figures.
Freshman forward Terran Alford also enjoyed a stellar performance, posting a near double-double with 10 points and nine rebounds while going 5-of-8 from the field. The Oklahoma City, Okla., native came up huge in the second half, scoring eight of 10 points in the final 20 minutes.
Fellow freshman Amanda Lawson also made contributions down the stretch, tearing down 10 boards to go with five points and four assists in 37 minutes of play.
White added six points, six rebounds, three assists and three steals in her final home game as a Cougar.
The Cougars shot a blazing 57 percent (13-of-23) from the field in the second half for a 48-percent clip (24-of-50) for the contest.
Houston limited UCF to just 33 percent (21-of-64) from the field and swatted five shots while almost breaking even on the glass by a 39-38 margin against one of the league's best rebounding teams.
The Cougars will look to carry their momentum into the regular-season finale at Tulane at 7 p.m., on Thursday.