Rapid Reaction: Royals 6, White Sox 3

CHICAGO -- The White Sox fell 6-3 to the Kansas City Royals on Sunday and were swept in a series for the second time this month.

How it happened: Home runs from Eric Hosmer (two-run) and Salavador Perez (three-run) helped the Royals to the victory. Andre Rienzo gave up six runs on six hits over six innings and added another four walks to boot. Adam Eaton opened with a leadoff triple and scored in the first inning, but the White Sox couldn’t keep pace despite 12 hits. Alejandro De Aza had a two-run double. The White Sox left 13 runners on base.

What it means: The White Sox are now a season-worst four games under .500 at 33-37. They had been three games under on three separate occasions, but each time they managed to win a game. It certainly could be worse, though. After a June 15 defeat to the Houston Astros last season, the White Sox fell to nine games under at 28-37 on their way to a 63-99 final record (36 games under).

Outside the box: A rainout last week gave the White Sox the opportunity to straighten out Rienzo, but the right-hander’s struggles continued. In his first start since June 6, Rienzo was only slightly better than he was while giving up seven runs on nine hits in 3 2/3 innings against the Los Angeles Angels. After starting the season 4-0, Rienzo has a 9.00 ERA over his last four starts, all defeats.

Off beat:Eaton prides himself on being the fly in the ointment and he was a real pest in the first inning Sunday. His ground ball ate up Hosmer at first base and rolled into the right-field corner, sending him off to the races. He ended up on third base and was generously credited with a triple on what looked to be an error. At third, he coaxed a pickoff throw from pitcher James Shields that ended up being a run-scoring balk. And to make Eaton’s pesky ways complete, it all ended with Royals manager Ned Yost getting ejected for arguing the balk call.

Up next: After a day off Monday, the White Sox will send left-hander John Danks (5-5, 4.17 ERA) to the mound Tuesday to face San Francisco Giants right-hander Matt Cain (1-4, 3.84) in the 7:10 p.m. start from U.S. Cellular Field.