CHICAGO— Right-hander Jeff Samardzija, who tossed a one-hit shutout in his previous outing, came back with seven strong innings allowing just two runs, and Adam Eaton slammed a two-run homer as the White Sox held off the Royals for a 4-2 win on Tuesday night at U.S. Cellular Field.

The Royals fell 1 1/2 games behind the Blue Jays, who were rained out, in the race for the American League’s best record and home-field advantage throughout the postseason. The Jays hold the tiebreaker based on winning the season series, 4-3.

Samardzija scattered eight hits, and the White Sox benefited from two great defensive plays to maintain the lead. Left fielder Trayce Thompson made a spectacular diving catch in seventh to rob Ben Zobrist of at least an RBI double. Then in the eighth inning with the potential tying run on second, Royals third baseman Mike Moustakas raked a liner toward left that third baseman Mike Olt speared on a lunge.