Chris Evans added 11 points and a game-high nine rebounds to help Kent State (8-5) win its fourth straight game.
Trailing 39-29 at halftime, Cleveland State (8-5) began the second half on a 12-4 run and got within two points, 43-41, on Tim Kamczyc's three-point play with 16:05 left to play.
Kent State answered, pulling away with a 28-10 run to take a 71-51 lead with 2:27 remaining.
Brewer led the Golden Flashes in the second half with 15 points, and Kent State connected on 15 of 20 free throws in the period to pull away with the victory.
Bryn Forbes led the Vikings with 12 points in their first home loss of the season.