CHICAGO -- The Rangers rallied back from multiple deficits and ultimately took the lead in the 10th inning in an 11-9 win over the White Sox at Guaranteed Rate Field on Saturday afternoon. But the tipping point, according to manager Chris Woodward, was Adolis García’s fifth-inning three-run home run.

Headed into the fifth, the Rangers trailed 5-0. Corey Seager’s sacrifice fly with the bases loaded trimmed the deficit to four runs, and that set up García’s blast to bring Texas within a run.

“That was the hit of the game to give us hope that we were going to come back to win that game,” Woodward said.

García’s homer was key to the come-from-behind win, but the White Sox added two runs in the bottom of the fifth to take a 7-4 lead. From there, Woodward turned things over to his bullpen, and their performance also helped put the Rangers in position to win in extra innings.

Jesus Tinoco, Brock Burke, Matt Bush and Matt Moore handled the sixth through ninth innings, holding the White Sox scoreless and earning 11 of the 12 outs via strikeout.

“Just wiping them out,” Woodward said. “Just set the tone and gave our offense the confidence.”

Moore was responsible for five of those 11 strikeouts, including an eighth-inning punchout of Luis Robert for his 900th career strikeout. Woodward praised Moore’s pitch mix against the White Sox, particularly the way he was able to use his fastball to set up his breaking pitches.

Given that the White Sox had a league-leading .287 batting average against left-handed pitching going into Saturday’s game, the lefty Moore’s ability to shut them down was integral to the win.

“He’s been honestly lights out for a while now. He’s made some pretty good hitters look silly,” Woodward said.

When Moore came into the game in the eighth inning, he was charged with protecting a 7-7 tie. Fighting back from a multiple-run deficit again, Brad Miller’s RBI single in the sixth and two RBIs from Kole Calhoun’s double and Jonah Heim’s sacrifice fly in the seventh had evened the score.

Moore struck out Robert and Jake Burger in the eighth and then fanned the side in the ninth, getting both Yoán Moncada and Reese McGuire looking.

“You always take pride in what you do well, you know, being able to step up for the club,” Moore said.

Rangers starter Martín Pérez has been one of the Rangers’ most reliable starters all season, but he struggled against the White Sox offense. Owning a 1.56 ERA going into the game, Pérez gave up a season-high 12 hits and six earned runs Saturday. Pérez said that some of his struggles were because home-plate umpire Alex Tosi’s strike zone was tight, but also because the balls Chicago put in play found the right spots in the field.

“They found the holes,” Pérez said. “I threw my sinkers down and away, and they hit the ball to second, and we have the shift, and there’s nothing you can do with that. That’s not an excuse, it’s just they hit the ball better against me.”

But because Pérez has consistently been the reason the Rangers have won games, the rest of the team felt compelled to lift him up.

“We got to pick each other up at times. He can’t carry us every time,” Woodward said.

The Rangers scored their decisive runs in the 10th inning to put the game away. Nathaniel Lowe led off with a double that scored the automatic runner, Charlie Culberson. Lowe later scored on a passed ball, and Marcus Semien drove in two more runs on a single to left field.

Those four runs in the 10th were made possible by the four runs Texas scored in the fifth and the bullpen’s shutdown work. The Rangers are 3-7 in their last 10 games and still sit four games below .500 and 8.5 games behind the Astros in the AL West, so a win like Saturday’s could provide an important spark.

“It’s how much fight you got in you, right?” Moore said. “It’s easy to fold. That’s the easy thing to do, is to just go home and take your beating, but these guys kept battling.”