With no outs and Jarrod Dyson on third, the White Sox brought their infield in, but it didn't matter one bit.
Gordon drove a 2-2 pitch from Donnie Veal (1-1) over the wall in center for his first homer since July 7 and No. 10 on the year.
Aaron Crow (7-3) tossed a scoreless inning to get the win and Greg Holland finished for his 27th save in 29 chances. Holland has converted each of his past 20 opportunities.
The White Sox had a chance to win the game in the 10th, but Dyson threw out pinch runner Blake Tekotte at the plate to end the inning. Tekotte was trying to score from second on Alejandro De Aza's sharp single to center field.
Kansas City (51-51) matched its longest winning streak of the season and got back to .500 for the first time since it beat Cleveland 2-1 on June 17 to improve to 34-34.
It's the best record for the Royals this late in the year since they finished the 2003 season with an 83-79 mark, according to STATS.
Adam Dunn homered for the last-place White Sox, who closed out a 3-7 homestand with their ninth loss in 12 games overall. Paul Konerko also had an RBI single.
David Lough, who made a terrific catch in the ninth inning of Kansas City's 1-0 victory on Saturday night, helped the Royals get off to a fast start in the series finale. He singled in Alcides Escobar with two out in the first, then walked and scored on Miguel Tejada's double in the fourth.
Dunn responded in the sixth, driving a 1-1 pitch from Bruce Chen over the wall in center to tie it at 2. It was Dunn's 25th homer of the season and No. 431 for his career, tying Cal Ripken for 43rd on the all-time list.
Dunn also helped set up Chicago's first run with a two-out walk in the first that moved Alex Rios into scoring position. Konerko followed with a run-scoring single into left field.
Chen allowed three hits, struck out five and walked two in six innings. The crafty left-hander has given up three runs in 18 innings over three starts since he returned to the rotation.
White Sox left-hander Hector Santiago struck out seven in 6 2/3 innings. He allowed five hits and walked four.
NOTES: White Sox RHP Jake Peavy brought a couple of big suitcases into the clubhouse before the game. He is scheduled to start on Tuesday in Cleveland, but he also is one of the top pitchers on the market ahead of Wednesday's non-waiver trade deadline. "I don't think he wants to go. I don't want him to go," manager Robin Ventura said. "But he has to be prepared. That's part of where we're at right now." ... Royals CF Lorenzo Cain got the day off after he left Saturday night's 1-0 win with tightness in his left groin. Kansas City is off Monday before beginning a three-game series at Minnesota, allowing Cain to rest for consecutive days. ... Chicago begins a four-game series against the Indians on Monday night. White Sox LHP John Danks (2-8, 4.81 ERA) opposes RHP Zach McAllister (4-6, 3.57 ERA) in the opener. ... Royals RHP Ervin Santana (6-6, 3.06 ERA) faces RHP Mike Pelfrey (4-8, 5.15 ERA) on Tuesday in Minnesota.