Soriano flagged down the threatening Jason Kipnis shot and threw a strike to first base for the second out of the ninth inning, then retired Asdrubal Cabrera and furiously untucked his jersey for his 33rd save in 35 chances this season.
In a season that has seen the Yankees already lose all-time saves leader Mariano Rivera to injury, any blow to Soriano during the stretch drive could be crippling; in 2006 with Seattle, Soriano's season ended after he was hit in the head by a Vladimir Guerrero line drive.
Fortunately, Soriano said that he had no trouble gripping the ball and said he expects to feel fine going forward.
"I [wasn't] scared at all," Soriano said. "I'm trying to find the ball and [get] people out."
Curtis Granderson hit his 200th career home run and Nick Swisher had three hits as the Yankees took two of three games in the weekend series from the Tribe, cleaning up a road trip that started with three losses to the White Sox.
They had to lean on their bullpen to do it. For the second time in as many starts, Freddy Garcia wasn't able to make it through five innings, but Boone Logan recorded five outs around one hit to step in line for the victory.
David Robertson followed with four outs of scoreless, one-hit relief before Soriano was called upon for a four-out save, the closer's third time this season recording a save of more than three outs.
"We all know what we're supposed to do," Robertson said. "We're supposed to come in, pitch as long as we can, get as many outs as we can and try to pass the ball to the next guy. I think that's the mentality everyone takes into the game."
New York touched Cleveland starter Ubaldo Jimenez for three runs in five innings, doing all of its damage in the second inning.
Ichiro Suzuki laced a run-scoring single to center field that tipped Jimenez's glove, and Derek Jeter knocked home a run with a groundout. Swisher followed with a line-drive single off Jimenez, who scattered eight hits with a walk and four strikeouts.
"You want to be able to capitalize on any opportunities you have, especially when you have guys on third with less than two outs," Jeter said. "You want to find out ways to get them in. Two-out hits are very tough to come by."
Granderson padded the lead with a sixth-inning solo home run, his team-leading 33rd, off Cleveland reliever Tony Sipp. After the game, a bottle of Moet & Chandon Champagne was waiting on ice at Granderson's locker in acknowledgment of his milestone blast.
"It's cool to have accomplished it," Granderson said of No. 200. "I didn't really know I was coming up on it until my aunt told me about it yesterday. It was neat to get it, and then I heard about the number of guys on our team that have done it, so the fact that we're all together on one team is pretty neat."
Despite an early hook, Garcia held the Indians to two runs and four hits. Cleveland loaded the bases in the third inning, helped by a Robinson Cano error, but couldn't score.
"Offensively, we just didn't execute very well early in the game," Indians manager Manny Acta said. "We had a couple of opportunities. We kind of let Freddy off the hook a couple of times."
Garcia ran into two-out trouble in the fifth inning, as Kipnis doubled and Cabrera was hit by a pitch. After a walk, Carlos Santana ripped a two-run single to end Garcia's outing. He tossed 90 pitches with two walks and six strikeouts, plus a hit batsman.
"Nothing surprises me at this point right now, man," Garcia said. "They made the decision, so there's nothing I can do about it. I'm just looking to my next start and trying to pass the fifth inning."
With the victory, the Yankees head home feeling thankful that their lead in the American League East -- now four games over the idle Rays -- was cut by only one game after their less-than-ideal road swing.
"We're really fortunate," manager Joe Girardi said. "We need to turn around, play better when we get home and put together a good series. Just continue to win series; that's the important thing, winning series."