The Brewers' bats took care of the rest.
"Yovani, huge game for us," Brewers manager Ron Roenicke said. "We were really thin in the bullpen today, and we really needed the length from him. And he also threw a great ballgame."
The Brewers bounced back from a demoralizing ninth-inning loss Tuesday night to take two out of three from the Blue Jays.
Gallardo (6-5) went 6 2/3 innings, giving up three runs and seven hits with two walks and seven strikeouts. Gallardo's outing provided some much-needed rest for Milwaukee's bullpen -- even if Gallardo didn't quite realize how dire the relief situation was.
"To be honest, I had no idea. But being a starting pitcher, obviously, you want to stay out there as long as you can. Obviously, the goal is to go nine innings every start. You know that's not going to happen 33, 34 starts, whatever it might be. But the deeper you get, the better, and the less the bullpen has to work."
With injuries testing the depth of Toronto's pitching, Milwaukee got to Blue Jays emergency starter Joel Carreno (0-2) early, hitting three home runs in a five-run second.
Braun extended his hitting streak to 15 games -- and 25 games in interleague play -- with a double in the third, then hit his 20th homer in the seventh.
Braun appeared to take a cleat to his right hand when he was thrown out at home in the third, but stayed in the game.
"It got me pretty good," Braun said. "It was a clean play, obviously, but it got in there pretty good. I'm all right."
Edwin Encarnacion hit his 20th home run of the season for the Blue Jays, a solo shot in the second.
The two teams combined for 16 home runs in the three-game series.
"I'm sure it's the pitching," Roenicke said of the power output from both teams. "If you go back and look at all the pitches that were hit out of the ballpark, there's probably not very many you'd say 'Hey, that's a good pitch.' "
Braun said temperatures in the 90s might have made a difference, too.
"The ball was carrying about as well as I can ever remember, between the warm weather and it seemed like there was a little bit of a breeze blowing out," Braun said. "And both offenses were really swinging the bat well."
Milwaukee then took the lead in the bottom half of the inning, beginning with Hart's solo homer and then the two-run homer by Maldonado. Gallardo followed with a double over the head of center fielder Colby Rasmus before Gomez homered to left, giving the Brewers a 5-1 lead.
Aaron Laffey came on in relief in the fourth after Carreno gave up five hits and five runs -- all on the three homers -- in three innings. With three starters injured, the Blue Jays turned to Carreno, a right-hander making his second career start.
"It's not the ideal situation when you have to take an overnight flight in here," Blue Jays manager John Farrell said. "That's the circumstances we're in. We're not going to use that as an excuse. It's not the ideal situation."
Milwaukee added another run in the sixth when Gomez walked, stole second base and scored on a bloop single by Nyjer Morgan that fell just inside the right-field line.
Gallardo cruised through the first two outs of the seventh, then gave up a single to David Cooper, a walk to Brett Lawrie and an RBI double to Rasmus to cut Milwaukee's lead to 6-2. Gallardo left the game to warm applause from the crowd and was relieved by Tim Dillard.
Dillard walked Jose Bautista to load the bases and face Encarnacion -- and Dillard hit him with a pitch, forcing in a run to cut the lead to 6-3. Dillard then struck out Kelly Johnson to end the inning.
Braun hit a two-run homer in the seventh to extend the Brewers' lead to 8-3.
Michael Fiers pitched a scoreless ninth for Milwaukee.
With two straight series wins, Gallardo sees the Brewers building some momentum.
"It's very important for us. It's obviously getting close to the All-Star break, and we (had to) turn things around quickly. We were able to do that this past six games, and we've just got to continue it."
Lawrie left the game with right knee soreness. Farrell said the move was precautionary and wasn't a major concern. ... The Brewers optioned Tuesday night's starter, Tyler Thornburg, to Triple-A Nashville and will make a corresponding roster move Thursday. ... Toronto claimed RHP David Pauley off waivers after the Los Angeles Angels had designated him for assignment. Toronto will make a corresponding move before Friday's game.