Robert McKiver scored a career-high 36 points, including 27 in the second half, as Houston overcame a 22-point deficit to win.
After Malone's 3-pointer gave the Cougars (8-9, 3-2 Conference USA) a 71-68 lead, the Golden Knights countered with a tip-in basket by Tony Davis.
With six seconds left, UCF (13-5, 3-2) fouled Oliver Lafayette. He made both free throws for the final margin. Jermaine Taylor's 3-pointer with a second to go bounced off the rim and UCF did not get another shot off before they buzzer.
McKiver made 11 of his 18 shots in the game including six of his game-high 11 3-point attempts. He also made eight of his nine free throws and led the Cougars with four assists.
UCF got 26 points from Robert Payne, 12 points from Taylor and 11 from Dave Noel. They were outscored 49-29 in the second half and 9-6 in overtime after racing out to a 35-15 lead at halftime.
The Golden Knights, who took their biggest lead of 45-23 with 13:50 left in the second half, held the Cougars to just 24 percent shooting in the first half and forced Houston to commit 10 turnovers.
The Cougars did not take their first lead of the game until McKiver made a one-handed jump shot with 3:05 left in overtime.
Dion Dowell was the only other Houston player to reach double-digits in scoring as Malone and Lafayette finished with nine points each. Lafayette, who recorded a game-high four steals, also recorded a game-high tying seven rebounds.