The Chippewas (10-14, 5-7 Mid-American Conference) trailed 66-65 before scoring the game's final six points. The Broncos went without a field goal for the final 2:11.
Central Michigan led 39-34 at halftime before Andre Ricks gave Western Michigan (11-14, 6-6) its first lead since the game's opening basket at 42-41. The Broncos held the lead until a Barrett dunk put the Chippewas ahead 56-54.
The score was tied four times and the lead changed three times afterward before Central Michigan pulled ahead for good.
Jordan Bitzer scored 12 points for the Chippewas. Barrett added seven rebounds for Central, which outrebounded Western 37-26.