It was the third triple-double for Whiteside, a freshman, who had 14 points, 11 rebounds and 13 blocks. Marshall (22-7, 10-4 Conference USA) set school records with 43 free throws and 67 attempts in stretching its winning streak to seven games.
The Thundering Herd led throughout the third OT, taking a 110-104 lead on Dago Pena's three-point play with 1:49 left. Marshall pushed it to 115-104 before UCF (13-15, 5-9) cut it to 117-113 on a 3-pointer with 32 seconds left.
Damier Pitts' four free throws sealed the win.
Pena scored 20, Pitts 19, Tirrell Baines 15 and Shaquille Johnson 13 for Marshall.
Taylor Young scored 23, Isaac Sosa 20, Keith Clanton had 20 and 12 rebounds, and Marcus Jordan 18 for UCF.