The Marlins snapped a three-game losing streak overall and a seven-game skid to the Reds.
Jeff Mathis, who was the center of Thursday's controversy at the plate, doubled to left to lead off the 10th off Sam LeCure (1-3), advanced to third on a sacrifice bunt by Reed Johnson, and scored on the base hit to center by Yelich.
Yelich doubled in the third inning and Jordany Valdespin drove him home with a single to center to give the Marlins an early 1-0 lead.
Eovaldi issued a leadoff single to Ramon Santiago in the seventh inning, ending his night. Bryan Morris came on in relief and Billy Hamilton hit a bloop single to left to score Santiago, who slid in safely at home to beat Yelich's throw and tie the game.
Mathis stayed back to wait for the throw, which could have affected the play. After the inning was over, Mathis was visibly frustrated in the dugout.
Giancarlo Stanton nearly hit a home run for the fourth consecutive game when he doubled off the right-field wall in the first inning.