Tyree Appleby scored on a short baseline jumper with 32 seconds left to give the Vikings (12-22) the lead.
Cleveland State then got a stop with 14.5 seconds left, Appleby missed the front end of a 1-and-1, and the Golden Grizzlies had a shot to win the game on the final possession, but the Vikings got another stop as time expired.
The Vikings, who upset top-seeded Northern Kentucky on Saturday, will face the winner of Wright State and Milwaukee in the championship on Tuesday.
Oakland (19-14) had the largest lead of the second half at 31-26 on Kendrick Nunn’s layup with 12:47 to go. Carpenter’s 3 cut the deficit to two and neither team led by more than a possession the rest of the way.
Nunn, the nation’s second-leading scorer entering the game (26.1 per game), finished with 19 points on 7-of-24 shooting. Jalen Hayes added 20 — the pair accounting for 39 of the Grizzlies’ 43 points.
The Golden Grizzlies were picked to finish atop the standings in the Horizon League Preseason Poll, but finished in fourth place, five games behind league champion Northern Kentucky. Oakland is now 2-5 in Horizon League Tournament history and 0-3 since it came to Detroit.
This is the third year Detroit has played host to the Horizon League Tournament, with games being played at Joe Louis Arena prior to this year. The tournament was previously hosted at campus sites before coming to Detroit. Due to low attendance, the tournament’s future in the Motor City is in limbo, according to The Detroit News’s Tony Paul.
© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.