The Royals, who have lost four of their last five, fell behind 3-0 after Adam Eaton drove a two-run homer into the bullpen in right field off Cueto (10-13) in the fifth inning.
Cueto lost for the third time in his four September outings and gave up three runs and eight hits over six innings. He struck out two and walked two.
Still a Royals offense that hadn't scored in 17 innings during a three-game stretch that included Kansas City being shut out 1-0 in 11 innings by the Chicago Cubs on Monday night, didn't do much to help Cueto - or the Royals.
Tuesday's loss dropped the AL Central champions to 10-17 in September. After beginning the month with a 6 1-2 game lead over Toronto for the best record in the AL, the Royals now trail the Blue Jays by 1 1-2 games with five games remaining in the regular season.
Asked if he's starting to fight the urge to try and do something to snap out of it, Royals manager Ned Yost said, ''Maybe a little bit, but we're not quite there yet.''
He added, ''We're fighting it a little bit.''
Kansas City got within 3-2 in the sixth when Hosmer and Morales homered off Samardzija (11-13), who won for the second straight time after losing nine of his 10 previous outings.
Coming off a complete-game one hitter against Detroit on Sept. 21, Samardzija scattered eight hits over seven innings to pick up the win, striking out two. The consecutive homers - Kansas City's first since July 25, 2014 - snapped Samardzija's string of 14 scoreless innings.
The solo homers didn't rattle Samardzija.
''That was the difference in the game,'' Samardzija said. ''You keep guys off the bases. If you pitch here in (U.S. Cellular Field) you're going to give up some homers, man. The ball flies. As long as no one is on base and they're solos, you can deal with it.''
The two solo shots were the only offense the Royals could muster. White Sox left fielder Trayce Thompson saved a potential game-tying run in the seventh inning with a full-extension diving catch that robbed Ben Zobrist of an extra-base hit that likely would have scored Alcides Escobar, who reached on a two-out single.
The Royals put a runner in scoring position in the eighth, but Chicago third baseman Mike Olt snagged a line drive by Mike Moustakes that appeared headed for left field.
''They made two great plays that saved them the game,'' Yost said.
Samardzija took care of the rest in picking up his first career win against the Royals.
''He's a guy, you usually face him and there's a good chance you'll get a fastball,'' Hosmer said. ''He was really mixing it up. Even in hitter's counts he had the ability to throw his off-speed pitches for strikes, which made him effective tonight.''
Royals: Morales (bruised right ankle) returned to the starting lineup Tuesday as the DH. Morales did not play Sunday after being hit by a pitch. He pinch-hit on Monday.
Royals: RHP Edinson Volquez (13-9, 3.65 ERA) will be looking for his first win since Sept. 8 after losing two of his last three starts. He will face White Sox LHP Jose Quintana (9-10, 3.38 ERA) who has taken no-decisions in his last two starts and who has only surrendered three earned runs in September.