The Yankees fell behind early on Thursday, with a shaky Nestor Cortes giving up three runs in the bottom of the first inning.
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The second wasn't any better for the left-handed pitcher, who gave up a solo home run to Astros outfielder Jake Meyers to make it 4-0 Houston.
But Cortes would settle down, allowing the Yankees to chip away at Astros' starting pitcher Framber Valdez.
The Bronx Bombers began their rally in the fifth, led by a bases-loaded RBI single from newcomer Juan Soto.
They would tack on two more runs in the inning before infielder Oswaldo Cabrera knocked a solo shot to tie the game at 4 in the top of the sixth.
Then in the top of the seventh, the Yankees would score the go-ahead run on a sacrifice fly from another off-season addition, outfielder Alex Verdugo.
The Yankees bullpen would take the lead from there and refused to relinquish it, with relievers Jonathan Loaisiga and Ian Hamilton pitching three combined scoreless innings.
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Things would get dicey though in the bottom of the ninth with closer Clay Holmes on the mound.
After giving up a leadoff single to Mauricio Dubon, the right hander would surrender another hit to Yordan Alvarez with one out.
With runners on first and second, Kyle Tucker then knocked a single to right field setting up the most dramatic play of the game.
With little margin for error, and with Dubon racing around third, Soto corralled the ball and fired a one-hopper to home plate.
The strong throw beat Dubon at the dish, but was slightly off the mark, forcing Yankee catcher Jose Trevino to dive to his left and pull off a nifty swipe tag on the runner attempting to slide around him.
The bang-bang play resulted in an out call by the ump, but Houston challenged the play.
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After a couple anxiety-inducing minutes -- the call was upheld after a review, leaving the Astros down to their final out.
With Alex Bregman at the plate with two outs, the third baseman hit a grounder to short that was easily handled by Anthony Volpe, who took the force out at second and solidified the Yankees 5-4 victory.
The win marked the fourth straight Yankee regular season win over the Astros, dating back to last September when they swept Houston in a three-game series.
The Bombers will now turn the ball over to left-handed pitcher Carlos Rodon on Friday, who will be on the bump to start the second game of the season.
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