The Racers (9-2), who led 36-34 at the half and won their ninth straight home game, took a 67-62 lead into the final 2 minutes before baskets by Danero Thomas, Canaan and Easley accounted for the game's final six points.
Murray State outshot Chattanooga (5-6) in the second half 60 percent (15-for-25) to 28.6 percent (10-for-35).
The Mocs held the upper hand in the early going, building an 18-8 lead with 12:45 remaining in the first half after Ty Patterson hit three consecutive 3-pointers.
Murray State took a 27-25 lead on Canaan's 3-pointer after a 19-7 run.
Patterson finished with 16 points and DeAntre Jefferson had 10 points and 11 rebounds for Chattanooga.