The 6-foot-7 sophomore made 11 of 16 shots, including a trey, and added 7 more from the foul line. He had company as the Mavericks (2-1) also got 19 points from Devin Patterson and 17 from Jake White, who scored 13 of his at the foul line.
Nebraska-Omaha went 36-for-48 from the free-throw line as 61 fouls were whistled during the game - 37 on UMKC, a school record.
Patterson made a layup and a foul shot to tie 83-83 in regulation. Thurman scored three jumpers in the OT.