Before the game, Gibbons said he overreacted when he tangled with Lilly near the dugout during Monday's game.
"I asked him if he wanted a piece of me," Gibbons joked of his mound visit to Burnett in the seventh.
Fans booed Gibbons when he made his first trip to the mound to talk to Burnett in the seventh inning. They cheered when he left Burnett in the game.
"As long as they recognize you, whether they are booing or cheering, at least they know you are around," Gibbons said.
Oakland manager Ken Macha jokingly said that if he listened to the fans, he would be sitting with them.
The A's tied an Oakland record for the biggest comeback victory by rallying from a 8-0 deficit on Monday, but their win was overshadowed by the scuffle between Lilly and Gibbons.
In July, Gibbons challenged Shea Hillenbrand to a fight after the infielder wrote on the clubhouse bulletin board that the "ship is sinking." Hillenbrand declined to fight and was later traded to San Francisco.
Toronto general manager J.P. Ricciardi said Gibbons' job was more secure than ever after the Hillenbrand confrontation. Asked if that is still the case, Ricciardi said it is.
But Ricciardi thought Gibbons made a mistake in confronting Lilly near Toronto's dugout.
"In hindsight he probably should have just went to the corner of the bench. I think he knows that too," Ricciardi said.
Burnett (6-5) allowed three runs and nine hits in 6 2/3 innings. B.J. Ryan pitched 1 2/3 innings for his 28th save in 32 chances.
"This was a good win for us after last night," Burnett said.
Wells' two-run homer off Brad Halsey (3-4) in the fifth gave Toronto a 4-1 lead.
Halsey allowed four runs and six hits in six innings in his first start since being recalled from Triple-A Sacramento. Halsey, who made 34 bullpen appearances for Oakland his year, made two starts in the minors to stretch his arm out.
"Not good. I wasn't good by any means," Halsey said. "My fastball command wasn't there."
Alex Rios hit a sacrifice fly in the fifth, and Wells followed with his 29th homer.
"I think we did a good job of focusing on today's game and you saw the result," Toronto's Reed Johnson said.
Burnett's run-scoring wild pitch and Mark Kotsay's RBI double in the seventh cut the lead to a run.
On Monday night, Oakland right-hander Dan Haren became the first pitcher in AL history to win a game in which he allowed eight runs over the first two innings, according to the Elias Sports Bureau. He's the first pitcher in the majors to do it since Rube Marquard of the New York Giants on May 14, 1913, against the Chicago Cubs.