The defeat drops Cleveland to 22 games below .500, tying a season-worst mark originally set on Sept. 2, when they were 56-78.
Pestano came on in the ninth inning with the game tied at 7 and made relatively easy work of the first two hitters he faced, needing a total of four pitches to retire them both.
Then Morneau blasted Pestano's first pitch -- a 92 mph inside fastball -- down the right-field line and into the seats. It was the left-handed slugger's second home run of the game.
"That's been the MO -- lefties always try to jump on me early, they don't really wait around," Pestano said. "I threw the pitch I wanted to throw. I didn't execute very well. He was able to get the barrel out and keep it fair."
Pestano said he looked to jam Morneau in the past, and even though he thought the Twins slugger would likely be expecting that, he hoped to turn Morneau's aggression against him.
His strategy was correct. But it backfired.
"I was looking for the pitch that I got -- just something to drive, something to pull," Morneau said. "I faced him a couple nights ago, he jammed me, so I had a feeling he might try to come in there again, and he did and left it over the plate just a little bit, and I just kept it fair enough and we get to jump up and down and have fun."
The pitch by Pestano was just one in a laundry list of poorly-executed pitches by the Indians, who called on five relievers after starter Corey Kluber struggled.
Cleveland spotted Kluber a 4-0 lead heading into the bottom of the third. But Kluber surrendered three runs in that inning -- one on Joe Mauer's RBI triple and two on Morneau's first home run of the day -- reducing the lead to 4-3.
Jason Kipnis' error allowed Darin Mastroianni to reach to start the fourth. He stole second, took third on Kluber's wild pitch, then came in to score on Pedro Florimon's bloop single to left. Ben Revere's ensuing RBI single gave Minnesota 5-4 lead and prompted Manny Acta to pull Kluber after he faced another batter.
Kluber became the third Indians starter in three games to fail to make it to the fifth inning, giving up five runs (four earned) on eight hits over 3 2/3.
"The guys did a great job early of giving me a lead," Kluber said. "I didn't do a good job of making it stand up."
The Indians answered in the fifth by taking a 6-5 lead after an RBI double from Carlos Santana and an RBI single from Russ Canzler. But more pitching mistakes saw them give it right back in the seventh.
Mauer rocketed a double on an 0-2 pitch from Esmil Rogers, moving Jamey Carroll to third. He intentionally walked Morneau to load the bases for Ryan Doumit as Tony Sipp came on for Rogers. Sipp retired Doumit via flyout, but Chris Parmelee tagged another 0-2 pitch for another two-out hit to score Mauer and Carroll, giving Minnesota a 7-6 lead.
Morneau's first home run also came on an 0-2 count.
"We gave up three 0-2 lasers that kind of cost us," Acta said. "The whole thing of pitching ahead and getting a guy 0-2 is to make a guy expand and try to make him chase and take advantage.
"We need to do a better job than that. If we don't execute in those situations, then we're going to pay for it as we did today."
The Indians did battle back yet again in the eighth. Jason Donald snapped an 0-for-17 slump with his second triple of the season, bringing Brent Lillibridge home to tie the game at 7. Lillibridge reached when he was hit by a pitch from Jared Burton.
Ezequiel Carrera nearly came up with the go-ahead hit in the ninth. He sailed a fly ball to shallow center with two outs and Vinny Rottino -- pinch-running for Matt LaPorta -- on third. But Revere made a tremendous diving catch to take the hit away and end the inning.
Santana delivered yet another big performance, going 3-for-5 and falling a triple short of a cycle.
It seemed like Santana and the Tribe might have another chance in extra innings. Then Morneau took that chance away.
"As soon as he hit it, I knew he got the barrel on it," Pestano said. "I watched it to see for a sec if it was going to be fair or foul. But it didn't take very long. So I wasn't going to wait around and watch them celebrate."