Morneau's game-winning blast -- and his second homer of the game -- came with two outs in the ninth inning on a first-pitch fastball from Pestano. It gave the Twins their fifth walk-off win of the year.
It was a special moment for Morneau, who is playing in September for the first time since '09, as he missed he missed September in '10 and '11 with concussion-like symptoms.
"Obviously the year hasn't gone as we'd hoped, but that's a team in front of us, and we're still playing for something," Morneau said. "We're a game behind them now, we've got a chance to catch them, so it's obviously. It's obviously not how we would have drawn it up, but days like this are nice, that's for sure."
Pestano was trying to jam Morneau with an inside fastball, but said it simply caught too much of the plate.
"I knew he was going to be aggressive," Pestano said. "I've tried to jam him every time I've had an at-bat against him, so I knew he was probably going to be looking for that. But I tried to use that to my advantage and be aggressive and get it in there. But he got the head out. Good hitters, when they guess right, they don't miss those pitches. That's exactly what he did."
The walk-off blast came after Parmelee laced a go-ahead two-run single in the seventh inning to give the Twins a one-run lead, only to see it blown on an RBI triple from Jason Donald in the eighth off reliever Jared Burton.
But with the help of a strong performance from the offense, the Twins were able to overcome a shaky outing from Esmerling Vasquez, who was making his second career start.
The right-hander lasted just three innings, allowing four runs on three hits and five walks, while striking out two.
"It just wasn't very fun to watch," Twins manager Ron Gardenhire said. "Kind of danced around the strike zone. You've got to do better than that."
Vasquez allowed the Indians to get out to an early lead with three runs in the second. Carlos Santana hit a solo shot, Shin-Soo Choo brought home a run on a sacrifice fly and a wild pitch from Vasquez allowed the third run to score.
Brent Lillibridge brought home another run for the Indians in the third on a sacrifice fly to score Michael Brantley, who led off the inning with a walk.
But the Twins came back with three runs in the third against rookie right-hander Corey Kluber. Joe Mauer brought home the first run of the frame on an RBI triple before Morneau blasted hit his first homer of the game, his 18th of the year.
Minnesota took the lead in the fourth when Pedro Florimon and Ben Revere each provided RBI singles off Kluber.
But the lead was short-lived, as Cleveland came back with two runs in the top of the fifth against reliever Anthony Swarzak. Santana plated a run on a double before scoring on a single from Russ Canzler.
The Indians had a chance to take a late lead in the ninth with a runner at third and two outs, but Revere made a diving catch in center field to rob Ezequiel Carrera of a go-ahead RBI single. It proved to be an important catch, as it set the stage for Morneau's walk-off blast.
"Benny came charging in on that one and make a heck of a catch," Gardenhire said. "He was playing shallow and the guy flipped it out there and it was diving. He got a heck of a jump on it and made a heck of a play. That's a game saver."