Josh Barfield singled home the go-ahead run in the 12th inning as Cleveland erased two deficits and survived a blown save to hold off Toronto 9-7.
"I can't say enough about the position players and how they just kept fighting back," Cleveland manager Eric Wedge said. "You're not going to ever see any more fight in a ballclub than what you saw with our guys tonight."
Grady Sizemore capped the rally with a two-out, two-run double into the right-field corner.
"We've been playing really hard and a lot of things haven't really gone our way in the first couple of months," Cleveland's Ryan Garko said. "It's nice to finally have some balls fall in and get some results."
Rafael Betancourt (1-1) pitched two innings for the win.
Jensen Lewis came on after Rafael Perez gave up three hits in the bottom of the 12th, including an RBI single to Rod Barajas, and got his first save by striking out Aaron Hill with runners at first and third.
"We haven't caught too many breaks until this point and we finally did," Lewis said. "It took everybody to win this game and we'll just use this momentum going into tomorrow."
Cleveland's first extra-inning win of the season came after a wild ninth inning when both teams came within a strike of victory only to blow the save.
Toronto answered with two runs in the bottom half against Cleveland closer Kerry Wood. With two outs and runners at second and third, Jose Bautista sent it to extra innings by lining Wood's 2-2 pitch into left-center for a two-run single.
The Blue Jays took a 2-0 lead on Barajas' sacrifice fly in the second and Adam Lind's RBI double in the third.
Toronto left-hander Brian Tallet didn't give up a hit through the first six innings but was roughed up in the seventh. Garko ended the no-hit bid with a one-out single up the middle and Matt LaPorta followed with a two-run homer to right, tying the game at 2.
It was the first career hit for LaPorta, a former first-round draft pick by Milwaukee who was dealt to Cleveland in last year's trade for CC Sabathia. LaPorta was called up from Triple-A on Saturday and made his major league debut Sunday.
"It's always big to get that first [hit]," Wedge said. "Obviously, his was a little bigger."
Tallet gave up a bunt single to Ben Francisco, a double to Sizemore and an RBI fielder's choice by Cabrera, giving the Indians a 3-2 lead.
"You hate to lose [the no-hitter], you'd love to throw one, but that's not the goal," Tallet said. "The goal is to win the ballgame and we just didn't do it tonight."
Toronto reclaimed the lead in the bottom half on a two-out, two-run single by Wells, chasing Indians starter Fausto Carmona.
Carmona allowed four runs and eight hits in 6 2/3 innings. He walked one and struck out three.
Tallet gave up three runs and five hits in a career-high seven innings. He walked three and struck out five.
Blue Jays LHP B.J. Ryan will head to Florida to began a minor league rehab assignment. Ryan, who has blown two saves in four chances, went on the DL on April 23 with muscle tightness in his back and shoulder. ... Toronto LHP Ricky Romero (strained muscle in his right side) threw his second bullpen session in the past three days and will begin a rehab assignment in Florida this week. ... Barajas has 12 RBIs in his last 11 games.