Yankees manager Joe Girardi and starting pitcher Luis Severino were ejected, as were New York pitching coach Larry Rothschild and bench coach Rob Thomson. No one from the Toronto side was tossed.
Third-base coach Joe Espada served as the Yankees' acting manager for the rest of their 7-5 win.
The first incident was precipitated by Blue Jays starter J.A. Happ hitting the Yankees' Chase Headley on the hip with his second pitch of the second inning after narrowly missing him with his first. The Yankees appeared to think this was retaliation for Severino grazing Josh Donaldson on the elbow pad with a pitch in the first inning.
"I was mad because Happ hit him on purpose and he had one shot," Girardi said after the game. "You throw it behind the guy and you miss, I mean, he's got to be tossed. That's terrible, it's terrible."
Happ denied that he was trying to hit Headley on purpose.
"I wasn't trying to hit Chase, but it happened," Happ said. "They can say whatever they want. Eventually cooler heads prevailed."
Both benches and bullpens emptied after Headley exchanged words with Happ, but order was quickly restored and plate umpire Todd Tichenor issued a warning to both benches.
"If they feel like they need to protect their guys, I respect that," Headley said. "But if you do that, you're accepting the consequences."
Things got much more heated in the bottom of the inning when Severino nailed Justin Smoak in the leg with his second pitch of the inning after narrowly missing him with his first.
This time, there were shoves on both sides after the teams came together, and at least one Yankee, Tyler Austin, appeared to be hit with a punch on his left cheekbone, which showed a bloody nick. The two catchers, Gary Sanchez and Russell Martin, also nearly came together but were kept separated by teammates.
"Some teams have been taking pot shots at us all year long, and some guys just got tired of it," Blue Jays manager John Gibbons said.
Blue Jays relief pitcher Joaquin Benoit limped off the field and into the clubhouse with a sore left calf following the second scuffle. Toronto then lost infielder Devon Travis with a sore shoulder in the sixth.
"In the pile, [Benoit] did something to his calf," Gibbons said. "He's getting checked out."
Gibbons didn't know whether Travis was hurt while taking part in a shoving match.
"I've got no idea," Gibbons said. "He came out of the game having trouble swinging the bat."
The testy behavior continued into the ninth. Leading 3-2, Gibbons called on Jason Grilli to close it out. But Yankees first baseman Mark Teixeira tied it 3-all with a one-out homer. After pausing to admire his second-deck drive and casually flipping his bat, Teixeira yelled "Blown save!" at Grilli after returning to the dugout.
"[The Blue Jays] do it all the time," Teixeira said, referring to his bat flip. "They have fun with it. It's the first time I've ever done it, so I'll have fun with it, too."
Headley called the Blue Jays "The Kings of Fun" for their emotional reactions to home runs and strikeouts.
"You've got to take some of your medicine," Headley said. "They certainly have no shortage of emotion, and if you play like that, you've got to expect to get some of it back."
Severino, who was making his first start since Aug. 13, was on a short leash to begin with and was expected to throw no more than 50 pitches. But his night ended after 34 pitches and one run allowed in the first inning.
It was Girardi's third ejection of the season; the last was Aug. 29 when he argued balls and strikes with plate umpire Brian O'Nora in Kansas City.
The Yankees had lost a record eight straight games in Toronto and 11 of 14 overall. The teams were playing for the 19th and final time this season.
Information from The Associated Press was used in this report.