With Celtics guard Kemba Walker driving toward the 3-point line, Butler deflected the ball with his hand - a legal play, upon review postgame. Walker was awarded a trip to the free-throw line and sunk all three shots to cut the Heat's lead to 109-107.
Butler then iced the Heat's victory with a pair of free throws of his own.
The league's report also indicated an additional pair of more minor incorrect calls earlier in the final minutes of regulation. With 1:27 remaining, Heat big man Bam Adebayo should have been whistled for a defensive three-second violation, and Celtics forward Jayson Tatum got away with a travel with 46.3 seconds remaining.
The Heat have a chance to finish the series in Game 5, which is slated for Friday at 8:30 p.m. ET.