They'll also receive undisclosed fines and both will appeal their punishments.
That pitch appeared to be in retaliation for Austin's hard slide in the third inning when his lead foot clipped the foot of Red Sox shortstop Brock Holt during a force out. Then in the seventh, Kelly hit Austin, leading to Kelly to slam his bat to the ground before coming after the pitcher.
New York's 10-7 victory against Boston would usually provide the headlines in normal circumstances, but in the seventh inning of the Major League Baseball clash all hell broke loose.
There was no knockout blow from the Red Sox.
In addition, Red Sox manager Alex Cora and Yankees third-base coach Phil Nevin were also fined along with Red Sox infielders Xander Bogaerts, Marco Hernandez and Dustin Pedroia and Yankees pitcher CC Sabathia, who were fined for leaving the bench while on the disabled list.
"I probably said something I shouldn't have to start the whole thing, so I'm sorry for that", Holt said.
One encouraging sign at the plate: After a slow start, Andrew Benintendi had his second multi-hit game in a row. Tyler Austin was forced at second base during a sacrifice bunt attempt.
In a matchup between teams that have long tangled, Gary Sanchez hit two home runs in a game that twice saw the benches empty and a fight that resulted in a trio of ejections.
While the New England Patriots are an epic source of pride, Beantown is a baseball town and now boasts the best team - or at least the best record - in the American League.
Afterward, the teams were split on the initial cause of the brawl, with the Yankees dismissing Austin's slide into third as a baseball play.
The scrawny right-hander, working about a 45-minute rain delay after the fifth inning, held the Yankees without a victor on the seventh inning until Aaron decide completed it using a double over the top of centre fielder Jackie Bradley Jr.
Tyler Austin reacts as he is ejected from the game.
However, Kelly and Austin will be eligible to play on Thursday after appealing the sanction. No other team since at least 1913 has begun a season with streak of 10 or more errorless games.
- After exiting Wednesday's game in the first inning, David Price is set to make his next start after a successful day of catch Thursday. He hit a batter enabled the enabled strikes, struck out 6 and had no walks.
In the visiting dugout, New York's pitchers have allowed 5.4 runs per game and its starters own a 4.24 ERA, 1.32 WHIP and 9.19 K/9.