CHICAGO -- The Chicago White Sox had a good idea of what they were getting when they added James Shields to their rotation in June.

Although the early returns came in a bit shaky and he was booed off the mound in his first start with the White Sox, Shields has made a drastic turnaround.

His latest outing may have been his best on a night when a drained White Sox bullpen needed a rest.

Shields threw 7 2/3 scoreless innings, and Adam Eaton homered as the White Sox earned their fourth consecutive win, 3-0 over the Chicago Cubs on Tuesday night at U.S. Cellular Field.

Shields left to a standing ovation after allowing only four hits while striking out five and walking four.

"Big Game James -- this was the guy we were thinking about when we got him," manager Robin Ventura said. "He came up big tonight.

"This is another (game) that we needed, and he came through for us."

David Robertson recorded his 24th save with a scoreless ninth inning for the White Sox (50-50).

Shields shut down the Cubs (59-40) before Nate Jones and Robertson closed out the win with hitless relief.

"He was a bulldog, man," White Sox third baseman Todd Frazier said of Shields. "He came out there and did what he had to do."

Shields snapped a personal three-game losing streak with the victory in which his curveball kept Cubs hitters off-balance all night. After throwing 56 pitches through the first three innings, Shields settled in and provided some much-needed relief for the White Sox bullpen, which had been overtaxed in recent days.

"I was trying to get ahead in the count," Shields said. "I had a little more walks than I wanted to today, but that's a good team over there. They work the count pretty good. Joe (Maddon, the Cubs manager,) has got them pretty much locked in as far as seeing pitches and really getting the pitch they want to hit."

It didn't matter Tuesday night.

The White Sox built a 3-0 lead in the sixth by taking advantage of control issues from Cubs reliever Travis Wood. With two outs in the inning, Todd Frazier singled off Kyle Hendricks (9-7) before Wood walked three straight batters to force in Frazier on Tyler Saladino's RBI walk.

That proved to be more than enough for Shields.

"They just outpitched us today," Maddon said. "We played well ... but we didn't score any runs."

Eaton gave the White Sox a 2-0 lead in the fifth inning with a solo home run off Hendricks, who had settled into a nice rhythm after giving up a run in the first inning.

Hendricks yielded a leadoff walk to Eaton in the first before Tim Anderson followed with a single and Jose Abreu delivered a one-out RBI single. A walk to Frazier loaded the bases, but Hendricks struck out J.B. Shuck to limit the damage to a single run.

The Cubs threatened in the second inning when they loaded the bases. Addison Russell singled, Miguel Montero walked, and Tommy La Stella was awarded first base on a catcher's interference call against Dioner Navarro. However, Shields got out of the jam when he got Dexter Fowler to pop out to Navarro to end the inning.

Hendricks gave up three runs on six hits and two walks in 5 2/3 innings. He struck out seven. As effective as Hendricks was, though, he wasn't any match for Shields.

"Listen, (Hendricks and Shields) pitched really well," Maddon said. "We just could not break through."

NOTES: Cubs 3B Kris Bryant was used as the designated hitter on Tuesday, as he still was not feeling 100 percent from a hard headfirst slide into second base in the ninth inning Monday. Manager Joe Maddon said Bryant's head took the brunt of the contact, but Bryant also was experiencing hand pain. Bryant went 0-for-4 with three strikeouts Tuesday. ... Cubs OF Jorge Soler (hamstring) needs between 15-20 more minor league at-bats before he will be ready to play again at the major league level. ... LHP Aroldis Chapman joined the Cubs on Tuesday after being acquired in a trade with the Yankees on Monday. ... White Sox LHP Carlos Rodon (sprained wrist) will throw a side session in the next few days after allowing three runs and five hits in 3 1/3 innings Monday in a rehab start for Triple-A Charlotte. ... White Sox 2B Brett Lawrie (hamstring) missed his fourth consecutive game.