The Bears (11-6, 5-1) moved a half-game over idle Weber State (10-6, 4-1) and a game ahead of Montana State (7-9, 4-2) and Montana (11-6, 4-2).
The Bears led 70-60 on Kai Edwards' dunk with 4:02 left before Montana State went on a 10-2 run. Harald Frey's 3 narrowed the deficit to 72-70 with five seconds left but Davis made 1 of 2 free throws before Sam Neumann turned it over for the Bobcats.
Montana State rallied from a 35-28 deficit at halftime with a 20-9 run and grabbed a 48-46 lead with 14:24 left when Keljin Blevins converted a layup. Hume responded with a 3-pointer, Trent Harris made back-to-back 3s and the Bears created some space with a 60-52 lead.
Harris added 14 points for the Bears and Jalen Sanders scored 10.
Tyler Hall led the Bobcats with 25 points on five 3s and Blevins grabbed 10 rebounds.
NCAA places Miss. State on 3 years probation
Mississippi State's football and men's basketball teams will not receive postseason bans in the aftermath of an academic scandal involving a tutor.
Scouting the draft: RJ Barrett projects to be even better in the NBA
ESPN NBA draft analyst Mike Schmitz explains how RJ Barrett's circumstances might have held him back at Duke.
Memphis will hold pro day for NBA teams featuring potential lottery picks
The pro day, featuring James Wiseman and Precious Achiuwa, will have a similar format to the draft combine.