CHICAGO -- Jeff Samardzija might not throw another pitch for the Chicago White Sox, so he made sure to leave the mound at U.S. Cellular Field on a high note Tuesday against the Kansas City Royals.

Samardzija, who can become a free agent in the offseason, allowed two runs in seven innings during the White Sox's 4-2 win in the series opener.

"He feels he figured out some stuff and feels good about it," Chicago manager Robin Ventura said. "It looks pretty crisp coming out of his hand. It's a tough lineup to go through. He's looked good these last two outings to let it go."

Samardzija (11-13), from nearby Valparaiso, Ind., threw strong outings in back-to-back starts to conclude his season, as he fired a complete-game shutout Sept. 21 at Detroit. He thinks a mechanical issue was the biggest reason for his struggles in the season's final two months, when he went 3-8 and dropped all six he started in August.

"It was just a simple fix with my mechanics, with where my hands were, to tell you the truth," Samardzija said. "They were getting away from my body, which was making me get around the ball and missing left and right and up in the zone mostly. So, I brought my hands a little tighter and it kept me a little more in line to the plate, and we started throwing more strikes ... more quality strikes."

First baseman Jose Abreu went 2-for-4 with an RBI single, shortstop Alexei Ramirez was 2-for-4 with an RBI double, and center fielder Adam Eaton went 2-for-4 and hit a two-run homer to lead the White Sox (74-83).

Chicago's bullpen preserved a slim lead, with three relievers combining to keep the Royals scoreless over the final two innings. Right-hander David Robertson retired the side in order in the ninth for his 33rd save.

Kansas City right-hander Johnny Cueto (3-7) allowed three runs on eight hits in six innings. The Royals have lost two games in a row, four of their last five, and they fell to 4-6 in their past 10 contests.

Manager Ned Yost admitted he is fighting the urge to do something to help the Royals (90-67) break out of their funk.

"Not quite there yet," Yost said.

Samardzija allowed eight hits, including back-to-back solo homers by first baseman Eric Hosmer (2-for-4) and designated hitter Kendrys Morales (1-for-3) in the sixth, but didn't walk anybody.

Yost, however, saw opportunities for the Royals to get to him that were prevented by two great defensive plays in key situations.

Chicago rookie Trayce Thompson made a great diving catch in left field to prevent a game-tying run in the seventh, and third baseman Mike Olt snared a line drive in the eighth that stranded two Royals runners.

"I'm seeing some pretty good at-bats, really," Yost said. "We had opportunities to win the game outside of two outstanding plays."

The Royals also got a great catch in the second when center fielder Lorenzo Cain robbed Thompson of extra bases with a leaping grab at the fence, but Thompson -- the younger brother of Golden State Warriors guard Klay Thompson -- got the last laugh. His catch in the seventh was the highlight of the game.

After a two-out single put speedy shortstop Alcides Escobar on first, Royals second baseman Ben Zobrist hit a line drive to the gap in left-center field. Thompson got a good jump and laid out to make a diving catch for the third out, preventing what would've been a run-scoring hit to tie the game.

Samardzija was fired up about it.

"He was happy," Thompson said. "The guy on first right there (Escobar), he can run. It's nice to help (Samardzija) out. He's one of those veterans who have been great to me."

Thompson also scored a key run in the eighth, when he walked and scored from first on a double by Ramirez that gave Chicago a two-run cushion.

The White Sox held a 3-0 lead after five innings, scoring on Abreu's single in the third and getting two more in the fifth on Eaton's 14th homer of the season.

NOTES: Kendrys Morales was Kansas City's designated hitter Tuesday. It was his first start since being hit on the right ankle by a pitch Saturday. Morales pinch-hit Monday at Wrigley Field after missing a game Sunday. ... White Sox manager Robin Ventura said there is a chance that rookie RHPs Erik Johnson and Frankie Montas could start the final two games of the season on Saturday and Sunday against the Detroit Tigers.