The late-inning heroics were provided by Alex Rios, who hit the go-ahead triple in the 10th inning off Indians closer Chris Perez.
"It was just part of baseball," Rios said to the Associated Press. "I was just trying to hit the ball hard somewhere and it worked out pretty good."
The Sox came out of the gate hot as they tagged starter Justin Masterson for two runs in the first inning. Gordon Beckham registered the first hit of the game and was moved over to third on Adam Dunn's booming double to center field.
A Paul Konerko groundout scored the first run, and a subsequent single by A.J. Pierzynski gave the Sox a 2-0 lead.
The score would remain 2-0 until the seventh when the Sox would manufacture a third run. Alejandro De Aza recorded his second single of the game and would later score on a Pierzynski groundout.
John Danks pitched seven strong innings but ran into trouble in the eighth after surrendering back-to-back singles to Casey Kotchman and Jack Hannahan. Chris Sale came on for Danks and forced Indians outfielder Johnny Damon to ground out to Alexei Ramirez—who subsequently booted the ball, loading the bases.
The Indians would score their first run as Kotchman would touch home on a Jason Kipnis groundout. A walk to Asdrubal Cabrera would reload the bases, which would be followed by a game-tying single by Carlos Santana.
Should Chris Sale Keep His Closer's Role?
The Sox were held at bay in the ninth but would get a strong showing by former closer Hector Santiago, who pitched a scoreless bottom frame.
The Sox would add an additional insurance run after the Rios triple. Santiago picked up his first win and Addison Reed pitched a flawless tenth for his second save.
"These guys didn't fold," manager Robin Ventura said, according to the AP. "They battled and did just a great job."
The White Sox are 4-6 in the last 10 games. Jake Peavy will take the hill tomorrow evening trying to earn a series split for the Sox.