"I'm pretty happy with the way the guys bounced back and took two out of three here," Indians manager Manny Acta said.
An 11-1 defeat in the opening game of the series was Cleveland's fifth loss in six games. But the AL Central leaders won 6-3 on Tuesday, then pounded out 18 hits to take the finale.
"Those two wins are huge," LaPorta said. "To do it the way we've done it, they're big wins for us."
Down 12-0, Toronto became the first major league team in 30 years to hit three straight triples. Eric Thames, Rajai Davis and Jayson Nix accomplished the feat in the fifth inning -- Montreal was the last club to do it, with Mike Gates, Tim Raines and Tim Wallach against San Diego on May 6, 1981.
The Indians scored four times while chasing Drabek in the first inning. LaPorta's shot highlighted an eight-run burst in the third.
Tomlin (7-2) allowed six runs and eight hits in six innings to match Boston's Jon Lester for the AL lead in wins. He walked one and struck out a career-high seven.
"It's definitely nice to have that run support early," Tomlin said. "It kind of frees you up to go out there and throw strikes and try to get ahead of hitters."
Davis homered off Tomlin and drove in four runs.
Cabrera went 4 for 6 and drove in two runs.
"He's been terrific," Acta said. "He's been the mainstay in our lineup every day since day one."
Winless in three starts, Drabek (3-4) allowed four runs and three hits. It was the shortest start of the rookie's career.
"This is absolutely the worst start I've ever had," Drabek said. "I've never in my whole life not gone at least an inning."
Manager John Farrell said the Blue Jays aren't losing faith in Drabek, the centerpiece of the trade that sent Roy Halladay to Philadelphia.
"We fully believe in him," Farrell said. "We fully expect that he's going to have some growing pains and we're fully aware of that and fully accepting of it. He is a guy that we're committed to."
Camp set down the first four batters he faced before the Indians erupted in the third, sending 13 batters to the plate.
Buck led off with a single, Santana walked and LaPorta hit a one-out drive off the restaurant beyond the center-field wall.
Hannahan doubled and scored on Adam Everett's single, Brantley singled and both runners on Cabrera's double. Shin-Soo Choo reached when Davis couldn't handle his liner to center and Buck was safe when shortstop Yunel Escobar dropped a popup in swirling winds, with each error costing Toronto a run.
The six-run outing raised Camp's ERA from 2.42 to 4.23.
Brantley's RBI grounder made it 13-3 in the top of the sixth. Toronto added three in the bottom half on Davis' first homer of the season, a drive to left off Tomlin.
Jose Bautista hit a two-run single off Hannahan's glove at third base in the ninth.
The Indians were two shy of their season high in hits. ... Cleveland has had two 10-run innings this season. They did it in the fourth inning at Seattle on April 8, and in the fourth inning at Kansas City on May 16. ... Bautista is the leading vote-getter among AL players in All-Star voting. He leads the majors with 20 home runs. ... Indians INF Orlando Cabrera got the day off after five straight games on artificial turf. ... Escobar went 0 for 3, snapping his hitting streak at a career-high 12 games. ... Thames had a career-high three hits.