CHICAGO – White Sox left-hander Chris Sale had a hunch that he would be locked in a low-scoring pitching duel Friday against former Cy Young Award winner Zack Greinke.

“With a guy like that across the way,” Sale said, “you know you have to bring your ‘A’ game.”

Unfortunately, none of Sale’s teammates remembered to bring their bats against the Milwaukee Brewers’ ace.

After neither team crossed the plate through nine innings, the Brewers scored in the top of the 10th and held on for a 1-0 win to take the series opener

 at U.S. Cellular Field. The Sox (36-34) fell 1½ games behind the first-place Cleveland Indians, who beat the Houston Astros to extend their lead in the AL Central.

Sox reliever Jesse Crain (1-1) was tagged with the loss after serving a leadoff double to Aramis Ramirez and a run-scoring single to Rickie Weeks in the 10th. Greinke (8-2) earned the win, and Brewers closer John Axford collected his 13th save.

Sox manager Robin Ventura said both starters deserved credit for attacking all parts of the strike zone and keeping hitters guessing. The Sox lost for the seventh time in their past nine games.

“You’re looking at two guys that can pitch,” Ventura said. “I think it’s one of those [games where] you just saw a great matchup and both of them just battling all the way.”

Sale dazzled a small but enthusiastic crowd of 22,798 during eight scoreless innings. In a 109-pitch performance, he allowed four hits and one walk while striking out seven.

“Everything was good,” said Sale, who lowered his already stellar ERA from 2.46 to 2.24. “Everything was right on point. I felt fine.”

Although Sale was excellent, Greinke was even better.

Greinke limited the Sox to three hits and one walk in nine scoreless innings. He did not allow a base runner to advance past first base while inducing three double plays and striking out four.

Sox shortstop Alexei Ramirez was one of six hitters to go 0 for 3 or worse against Greinke. Ramirez managed two flyouts and a groundout as Greinke breezed through nine innings on 100 pitches.

“Greinke came with his arsenal,” Ramirez said through a translator. “He made really good pitches and made it really hard to try to get ahead.”

Much has been difficult for Sox hitters as of late. They have scored one run or less in three of the past five games, and Friday marked the seventh time this season in which they were shut out.

Despite the drought, Ventura said he believed that his team was capable of winning low-scoring contests. They rank fifth in the American League with 85 home runs but have struggled with a .202 batting average and 26 runs in their past nine games.

“We have the ability to hit home runs and things like that,” Ventura said. “I think tonight, it was more of the pitching than it was anything else. …

“There will be a period of time you go through as a team, as an offense, that it just doesn’t work for a little while. But we’re equipped to play whatever way you want.”