Keller and Anderson were ejected by home plate umpire Joe West after the fracas. Royals skipper Ned Yost and White Sox manager Rick Renteria got into it with each other, and Renteria and Royals coach Dale Sveum were also ejected, according to Daryl Van Schouwen of the Chicago Sun-Times.
White Sox shortstop Anderson may have gotten under the skin of his opponents by uncorking an emphatic bat flip following a two-run homer off Keller earlier in the game.
Keller hit Anderson with the first pitch of the shortstop's next at-bat with the game tied 2-2.
It's not the first time the 25-year-old has ruffled the Royals' feathers. In April 2018, Kansas City catcher Salvador Perez disapproved of Anderson admiring a long home run. Anderson assured critics that he wasn't about to tone it down.
"I led off the game with a home run and got excited," Anderson said at the time, according to Van Schouwen. "They didn't like it, but it's not about them, it's about my teammates. I play the game with a lot of energy and confidence. I'm not going to change."
Wednesday's game is the last in a three-game set between the clubs. Their next encounter comes May 27-29 when the Royals return to Chicago.