Shields (2-7) gave up one run and four hits in seven innings after going 12 starts and 13 appearances without a win. The veteran right-hander struck out two and did not walk a batter in his first victory since the opener at Kansas City.
Moncada and Sanchez connected on consecutive pitches from Adam Plutko. Matt Davidson drove RBI doubles off the center-field wall in both the first and a two-run fifth, and the White Sox beat the AL Central leaders after losing their first four meetings this season.
Recalled from Triple-A Columbus, Plutko (3-1) got tagged for five runs and eight hits in 4 2/3 innings. The 26-year-old righty won his first three major league starts this season before getting knocked around by Chicago.
The Indians got a sacrifice fly from Jose Ramirez in the sixth and had runners on first and third with one out in the ninth, but came up short after winning five of six.
Xavier Cedeno struck out Jason Kipnis before Joakim Soria retired Yan Gomes on a fly to the center-field warning track for his ninth save in 11 chances.
The Indians optioned catcher and outfielder Francisco Mejia back to Triple-A a day after recalling him, because catcher Roberto Perez did not need to go on the disabled list. Perez was hit by a pitch in the right wrist against Detroit on Sunday.
Indians: 2B Jason Kipnis (neck) was back in the lineup after sitting out the previous two games and so was 1B Edwin Encarnacion (ankle) after missing three in a row. ... The Indians continue to hold off on activating OF Brandon Guyer (strained neck) after he was hit in the wrist by a pitch during a rehab game for Columbus on Sunday. Manager Terry Francona indicated they might wait until Thursday, when the White Sox send a lefty to the mound in Carlos Rodon. ''We're just trying to make sure he's ready,'' Francona said.
White Sox: OF Avisail Garcia (strained right hamstring) went 1 for 2 for Triple-A Charlotte against Durham in his first rehab game on Tuesday.
Indians: RHP Trevor Bauer (5-4, 2.62 ERA) hopes to continue his mastery over the White Sox after going 2-0 with a 2.19 ERA in two starts against them last year.
White Sox: RHP Dylan Covey (2-1, 2.22) tries to build on another strong outing after throwing three-hit ball over six innings in a 1-0 victory over Chris Sale and the Red Sox at Fenway Park on Friday.
More AP baseball: https://apnews.com/tag/MLBbaseball