Several punches were thrown and a couple of players were tossed to the ground once the benches and bullpens emptied.
The problems started when Gomez paused at the plate and flipped his bat after hitting a two-out drive in the third inning off Pirates starter Gerrit Cole. The ball hit the wall and Gomez sped into third base, making a head-first slide for a triple.
Cole, who was near third base backing up the play, stormed toward Gomez and they exchanged words.
Gomez took a couple steps toward Cole before players rushed the field from both dugouts. Milwaukee's Martin Maldonado threw a punch that knocked off Snider's hat.
Snider, who wasn't in the game, and Gomez shoved each other, and the Brewers star fell to the ground. Pirates catcher Russell Martin had to be restrained by teammate Gaby Sanchez as he walked off the field.
Brewers bench coach Jerry Narron also was ejected.