In total, 14 players and staff were disciplined for their roles in the brawl at Globe Life Park in Arlington, Texas.
Rangers shortstopElvis Andrus was suspended one game for his "aggressive actions during the incident." Andrus served his suspension Tuesday in Oakland.
"The rules are fair for punishment," Rangers manager Jeff Banister said. "They are in place for a reason. We'll live by them and move on."
Blue Jays manager John Gibbons was suspended three games. He had been ejected earlier in Sunday's game but returned to the field. First-base coach Tim Leiper was handed a one-game ban for returning to the dugout after his ejection. Both were fined undisclosed amounts.
Bench coach DeMarlo Hale will manage the Blue Jays while Gibbons serves his suspension, which began Tuesday night with a 12-2 loss toTampa Bay. Assistant hitting coach Eric Owens coached first base in Leiper's place.
Gibbons, who was suspended one game in August for returning to the field during an altercation with Kansas City after he was ejected earlier in the game, said he was surprised by the length of his suspension this time.
"I thought that was a little excessive," Gibbons said. "But what are you going to do? I've got enough issues to worry about."
Even though he knew he would be punished, Gibbons said he returned to the field to calm the situation and protect his players.
"That's your team out there," he said. "It makes sense to me that you should go out there and try to keep things under control, but that's not the rules, so you've got to live with that."
Gibbons would not say whether he thought eight games was a fair penalty for Odor.
"I can't worry about him,'' Gibbons said. "I've got to worry about myself."
Odor was fined $5,000, according to Yahoo! Sports. He and Bautista both appealed their discipline.
"I knew I was going to be suspended,'' Odor said before Texas' 8-5 loss to Oakland, which came on a walk-off grand slam byKhris Davis. "I have to follow the rules, and I'm just waiting for the appeal. I want to be with my team all year. I don't want to be out eight games."
Bautista was in the lineup Tuesday against Tampa Bay and hit a two-run homer in the first for Toronto's only runs on the night. Afterward, the slugger said he was "confident" in his appeal.
Bautista slid at Odor's legs in the midst of a double play Sunday in the top of the eighth inning of the Rangers' 7-6 win. Players from both teams rushed the field, and Odor shoved Bautista and then landed a punch to his face. Bautista had reached base after being hit by a pitch from Matt Bush.
Odor said Monday he didn't regret hitting Bautista.
Many players were involved in the melee. Bautista and Odor were ejected after the brawl, as were Toronto third baseman Josh Donaldson and Texas bench coach Steve Buechele, who were fined Tuesday.
Donaldson offered mostly one-word answers when asked to comment on the rulings. Asked whether he considered the tension between the Blue Jays and Rangers to be over, Donaldson said "sure."
Other players who received fines included Rangers pitchers Bush, Sam Dyson (aggressive actions) and A.J. Griffin (being on the field while on the DL); Rangers catcherRobinson Chirinos(being on the field while on the DL); and Blue Jays outfielder Kevin Pillar (aggressive actions).
"I wish I struck out Pillar and not given up a run,'' said Bush, who made his big league debut last week. "Other than that, I think I handled the situation very well. I'm having fun."
Umpires needed about 10 minutes to restore order after the brawl. When the game resumed, Blue Jays reliever Jesse Chavez hit Prince Fielder with the next pitch, which caused both teams to leave their dugouts again, though no punches were thrown that time.
Chavez and Hale were ejected. Hale was serving as acting manager after Gibbons was ejected in the third inning for arguing balls and strikes.
Chavez was handed a three-game ban, which he appealed, for intentionally throwing at Fielder. Hale was fined for Chavez's intentional actions after teams had been warned by umpires.
Despite punching him, Odor said Monday that he respects Bautista because he "plays hard."
The Rangers' series-clinching victory Sunday was the final regular-season meeting between the two clubs. A feud had been simmering between the teams since Bautista's bat flip in last year's American League Division Series.
Information from The Associated Press was used in this report.
Ravech: Odor should have gotten 10 games
Karl Ravech reacts to MLB's decision to suspend Rougned Odor for eight games for punching Jose Bautista on Sunday.
Benches clear after Odor slugs Bautista
The benches clear between the Blue Jays and Rangers after Jose Bautista slides into second base and gets punched in the face by Rougned Odor.