Yoán Moncada had two RBIs as Chicago won for the fourth time in five games. Andrew Benintendi and Luis Robert Jr. each scored two runs.
Burger has hit safely in six games since returning from a strained left oblique, going 11 for 22 with three homers and nine RBIs. He came through again in this one, breaking open a tight game.
“For me, it's just controlling everything and slowing the game down,” Burger said. “I feel like I did that in the last at-bat real well."
With Chicago ahead 2-1, its first three batters reached in the sixth before Royals starter Jordan Lyles was replaced by Jose Cuas. Benintendi walked and Robert reached on catcher interference before Moncada walked.
After Andrew Vaughn struck out swinging, Burger hit a liner into the gap in right-center. Burger’s clutch swing gave the White Sox a 5-1 lead.
“It's a one-run game and you've got to have some extra focus, especially in that situation,” Burger said. “Fortunately I got the right pitch and drove the ball to right-center.”
Giolito (3-3) permitted one run and six hits in six innings. The right-hander has a 2.66 ERA his last eight starts.
“For me it's all about taking it one pitch at a time, executing and working well with Seby (catcher Zavala) on sequencing,” Giolito said.
Salvador Pérez hit his 10th homer in Kansas City's sixth loss in eight games. Pérez finished with three hits, including a double, off Giolito.
“With Salvy, he's owned me over the course of my career,” Gioloto said,. “Some days it's like I strike him out out two or three times in three at-bats. Other days it's like homer, double, double. Today was one of those days.”
Pérez was a lone bright spot for the last-place Royals.
“He's a good ballplayer man," Kansas City manager Matt Quatraro said. “It's no accident he's been doing this for 12-13 years.”
Royals right-hander Jordan Lyles (0-8) was charged with five runs, four earned, and four hits in five-plus innings.
Pérez drove a 3-2 slider just over the fence in left-center in the first for Kansas City
But the White Sox responded with two runs in the bottom half.
After Benintendi singled and Robert doubled, Moncada hit a two-run single to left.
White Sox closer Liam Hendriks, who is recovering from stage-4 non-Hodgkin lymphoma, is expected to throw another live batting practice session, possibly when the team is in Cleveland for a three-game series that starts Monday.
Manager Pedro Grifol said the team and Hendriks will evaluate his status afterward and “we’ll see where we go from there.”
The 34-year-old right-hander tossed live BP in Chicago on Friday and was back in the clubhouse on Saturday.
Kansas City reinstated left-hander Amir Garrett from the family medical emergency list and optioned right-hander Jackson Kowar to Triple-A Omaha. Kowar made his season debut in Friday’s 2-0 loss at Chicago, pitching 2 1/3 scoreless innings.
White Sox: OF Gavin Sheets was scratched. He jammed a wrist sliding into second on Friday. ... C Yasmani Grandal (right hamstring) was available off the bench. He is expected to start Sunday. ... OF/DH Eloy Jiménez (appendectomy on May 6) has resumed all baseball activities and “is probably ahead of schedule,” Grifol said. ... INF Elvis Andrus (oblique strain) has resumed batting practice.
White Sox right-hander Lance Lynn (2-5, 6.66 ERA) pitches in the series finale on Sunday. The Royals had not yet named their starter.
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