CLEVELAND -- The Chicago White Sox snapped their seven-game, head-to-head losing streak against the Cleveland Indians in the grandest way possible: with a slam.

Adam Eaton's grand slam with one out in the ninth inning capped a five-run rally that gave the White Sox a 10-7 victory over the Indians on Wednesday night at Progressive Field.

"Nobody gave up," White Sox manager Robin Ventura said. "Guys just kept grinding, all the way through."

The win went to Jacob Turner (1-1), who pitched a scoreless bottom of the eighth. David Robertson pitched the bottom of the ninth to pick up his 30th save of the season.

Cleveland went into the ninth inning with a 7-5 lead. Closer Cody Allen (2-5) struck out the first batter of the ninth, but Todd Frazier reached on an infield single and went to second on a throwing error by shortstop Francisco Lindor. J.B. Shuck reached on an infield single to second. Tim Anderson walked, loading the bases.

Dioner Navarro hit a popup behind third base that fell in safely for a single, scoring Frazier to cut the lead to 7-6 and leaving the bases loaded. Eaton then belted an 0-2 pitch from Allen into the seats in right field for his first career grand slam.

"Two infield singles, a walk, a flare, Cody gets up 0-2 then hung a breaking ball, and that was the ballgame," Indians manager Terry Francona said.

Allen said, "I didn't think it was that bad a pitch. He just put a good swing on it."

Ventura liked Eaton's approach in the at-bat.

"He wasn't trying to hit a home run, and good things happen when you do that," the Chicago manager said.

Eaton added, "That was a lot of fun. Give credit to the guys ahead of me who put me in that position."

The White Sox came into the game with a 2-8 record against Cleveland this year.

"This shows the fight that this team has," Eaton said. "In the ninth, it would have been easy to go one, two, three, and just lay down. But we didn't give up. It was a total team effort."

Cleveland's 7-5 lead was forged by Brandon Guyer, who had three hits and two RBIs, and Lonnie Chisenhall, who had three hits and three RBIs. Chisenhall and Carlos Santana homered for the Indians, who got an up-and-down start from Carlos Carrasco.

Carrasco had 11 strikeouts and no walks in 6 2/3 innings. However, he gave up five runs (four earned) and eight hits.

"That was the best stuff we've seen from him this year," Francona said. "He just made some pitches in poor locations and paid the price."

Anthony Ranaudo was recalled from Triple-A Charlotte to start for the White Sox, and it was a brief evening for the big right-hander. He threw 88 pitches in four innings and gave up five runs on eight hits.

"He did all right. That's a tough offense," Ventura said. "He was up with his pitch count, but that's what a good lineup does."

A two-run homer by Chisenhall gave the Indians a 2-0 lead in the second inning. The White Sox tied it with a two-run home run by Anderson off the left field foul pole in the third.

A solo home run by Santana and an RBI single by Chisenhall gave Cleveland a 4-2 lead in the third inning. The White Sox scored three in the fourth, two on a double by Frazier, to take a 5-4 lead.

"It was like a boxing match from the beginning," Eaton said.

Cleveland tied it in the bottom of the fourth on a sacrifice fly by Jason Kipnis.

Guyer's two-run single in the fifth, his third hit of the game, pushed the Cleveland lead to 7-5, and it stayed that way until the ninth inning.

NOTES: Indians RHP Josh Tomlin was placed on the family medical emergency list and returned to his home in Tyler, Texas. The Indians will fill Tomlin's spot on the roster Thursday with the activation off the disabled list of RHP Danny Salazar, who will start Thursday night's game. ... The Indians entered Monday with a record of 24-9 (.727) at home since June 1. That was the second-best home record in the majors in that span behind Baltimore's 22-8 (.733). ... RHP Anthony Ranaudo was recalled from Triple-A Charlotte to start Wednesday's game. Ranaudo took the spot of RHP Carson Fulmer, who was optioned to Charlotte. ... White Sox LHP Jose Quintana has won nine games in each of the last four years, and he has nine wins this year.