Mets pitcher Noah Syndergaard knocked down shortstop Alcides Escobar with the first pitch of the game, a 98mph fastball that whizzed past his head.
Syndergaard said he had thrown the ball to "make a statement".
The Mets trail the best-of-seven series 2-1, with the fourth game taking place at Citi Field on Saturday night.
Royals third baseman Mike Moustakas said his team were "upset" by Syndergaard's actions, adding: "All 25 guys in that dugout were pretty fired up."
Escobar added: "The first pitch around my head, that's not good."
The pitch set the tone for the game, in which the teams traded leads in the early innings, before the Mets pulled away.
The Kansas City Royals were angered by aggressive tactics from the New York Mets as they lost game three of the World Series 9-3.