It was Cuddyer's leaping catch against the tall blue wall in right, though, that really saved the game and served as one of the best and most important defensive plays in Minnesota's so-far middling, frustrating season.
The Twins moved within 5½ games of the Indians, who began the day in first place in the AL Central.
"It was an exciting win. I was out there in the ninth inning giving fist bumps when we got that last out," said Cuddyer, who came off the disabled list and had two hits on Friday.
Cleveland was leading 1-0 and the bases were loaded against Garza in the fourth when Casey Blake's drive sent Cuddyer hustling back to the warning track. He braced himself, jumped and caught it with his back pressed against the wall, minimizing the damage to a go-ahead sacrifice fly.
"That was probably going to be a base-clearing double," Garza said, adding: "I got lucky."
Cleveland starter Aaron Laffey (0-1) made his major league debut, but he didn't quite get enough hitting help. Laffey gave up six hits, three runs, and one walk while striking out three.
"He did a great job for the first time out, gave us every opportunity to win the ballgame," said Indians manager Eric Wedge, whose team dropped to 7-3 against the Twins this year.
The 22-year-old Laffey, who went 11-4 with a 2.99 ERA while pitching for Double-A Akron and Triple-A Buffalo, took his first loss since May 28 -- just his third start after the promotion.
His young face looked calm through the 5 1/3 innings he lasted, and Wedge shouted encouragement when he gave him the hook in the sixth in favor of Jensen Lewis. Laffey was close to coming out with his first victory, but a balk and a couple of not-so-perfect pitches cost him.
"They hit mistakes up here, and I have to learn from that," Laffey said.
It was 2-all when Jason Tyner was hit by a pitch leading off the sixth, and he took second when Laffey flinched his shoulder before a pickoff throw and was called for the balk. Joe Mauer's single sent Tyner to third, and Lewis' first pitch was hit hard by Cuddyer to third base.
Casey Blake snagged the ball on one hop and threw to second for the forceout, but Tyner crossed the plate and the Twins took a 3-2 lead.
They scored twice in the fourth, when Jason Bartlett's double set up Mauer's rolling RBI single that second baseman Josh Barfield couldn't stop with his glove. Cuddyer came next with a double that scored a sliding Mauer.
Garza's ERA is still only 1.78, but this was his shortest start since he was called up at the end of June. He threw 93 pitches and only 55 strikes in four innings, loading the bases twice.
That was enough trouble for manager Ron Gardenhire, who sent Ortiz out to start the fifth. Garza gave up six hits and walked two while striking out five. He hasn't won since July 6.
Victor Martinez hit a two-out double that drove in a run in the third, but Cleveland stranded eight runners in the four innings against Garza.
"We were about one or two big hits from blowing that game open," Blake said.
After Cuddyer's big catch, Minnesota's bullpen made sure that didn't happen. With Jesse Crain out for the season and Juan Rincon struggling, the Twins have had to shuffle roles around. But with a lagging lineup and an inexperienced rotation, the relievers have again been the team strength.
"They've been very, very good," Gardenhire said.
- Indians LHP reliever Jason Stanford was designated for assignment to make room on the roster for Laffey. He's expected to become a free agent.
- The Twins optioned OF Lew Ford after the game and planned to call up LHP Carmen Cali.
- Mike Redmond was behind the plate for Minnesota, with Mauer serving as the DH. This was Redmond's 61st game this season, compared to only 47 last year.
- Laffey was the youngest Cleveland starter to debut since a 20-year-old C.C. Sabathia first appeared in April 2001.