Anderson is expected to miss six weeks with a tear in the middle finger of his left hand. He was put on the 10-day injured list betwen games of the twinbill.
Anderson was injured on a check swing during his last at-bat on Saturday night at Texas. He will have surgery on Thursday in Chicago.
''Huge blow. He's one of our All-Stars and one of our leaders,'' losing pitcher Lance Lynn said.
Anderson, who is hitting .301 for the playoff-contending White Sox, didn't play while finishing up a two-game suspension for making contact with an umpire.
Pratto homered, doubled and singled. He began the day batting .186 (11 for 59) this season in 19 games. His third homer put the Royals ahead 4-1 in the sixth.
Brady Singer (5-4) allowed one run on five hits in 7 1/3 innings. He struck out six without walking anyone.
Jose Cuas picked up his first career save.
Lynn (2-5) allowed two-run homers by Pratto and Vinnie Pasquantino in six innings.
Josh Harrison hit a solo homer in the Chicago third. Pasquantino homered in the bottom half.
The White Sox threatened in the sixth, getting two-out singles by Luis Robert and Eloy Jimenez. But Singer got Jose Abreu to line out to end the threat.
Yoan Moncada had a sacrifice fly in the ninth for the White Sox.
Chicago: RHP Davis Martin was recalled from Triple-A Charlotte to serve as the 27th man in the doubleheader.
Kansas City: RHP Jonathan Heasley was recalled as the 27th man for the doubleheader. He was the scheduled starter for the second game of the doubleheader. . RHP Taylor Clarke was placed on 15-day injured list (retroactive to Aug. 8) with a left oblique strain. He was replaced on the roster by Cuas, who was recalled from Triple-A Omaha.
The White Sox and Royals will continue their four-game series Wednesday night. RHP Johnny Cueto (4-5, 2.91 ERA) will start for Chicago. LHP Kris Bubic (2-6, 5.27 ERA) will get the start for the Royals.
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