CHICAGO -- Even though the rebuilding Chicago White Sox will miss the playoffs and narrowly avoid 100 losses this season, they've had plenty of individual highlights.

For one, outfielder Avisail Garcia has extended his career-high totals for home runs (18) and RBIs (80).

"I'm just thankful and I got to keep the same routine, the same everything, and work hard every day, every year, every month so I can bring the best for my team," Garcia said.

Garcia hit his 18th home run and Lucas Giolito threw seven strong innings to lead the White Sox to an 8-1 victory over the Kansas City Royals on Sunday afternoon, hurting the Royals' playoff chances.

Garcia drove in three runs and Kevan Smith had two RBIs for the White Sox, who have won three of four and nine of their last 15.

Lorenzo Cain homered for the Royals, who fell to 5 1/2 games behind Minnesota for the second American League wild card with seven games remaining.

Giolito (3-3) struck out five and gave up one run, five hits and no walks in seven innings. He has pitched seven innings in three of his seven starts this season.

"I feel like I belong," Giolito said. "I feel like this is where I can pitch. I can pitch deep into games. I wouldn't really say awestruck or anything like that. There were a lot of struggles early this year, and I worked through those."

Giolito has allowed four runs in his last 20 innings.

"I felt I was throwing a little bit harder today in the first inning," he said. "It's the end of the year, I have one more so I'm just trying to get into my legs and drive the ball through the strike zone. I felt like we did a good of that. Smitty (Smith) called a really good game again back there. I don't think I shook off a pitch the entire time."

The Royals finished with just five hits overall.

"He was pretty good," Royals manager Ned Yost said of Giolito. "We've been swinging the bats OK. He just shut us down."

Royals starter Ian Kennedy (4-13) allowed five runs and seven hits in 5 1/3 innings to drop his seventh straight decision. He pitched one day after traveling from Kansas City after the birth of his first son.

"It's frustrating," said Kennedy, who has been dealing with shoulder fatigue. "The whole plan missing that start was to feel better. It's more frustrating when you do feel good or you feel better than you have in the last month or so, and you're not getting the results you're hoping to get. Just happy to go home and see my little boy."

In eight previous career starts against the White Sox, Kennedy was 2-2 with a 4.63 ERA.

"First inning, I didn't think he was real sharp, made a mistake up and in to Garcia," Yost said. "But after the first inning, I felt like he was much, much better. Another mistake on a breaking ball for a home run, but got us into the sixth inning with an opportunity. We just couldn't generate any offense."

Garcia hit a two-run home run after Yoan Moncada doubled in the first inning.

Cain led off the fourth inning with his 15th home run to cut the lead in half.

In the bottom of the fourth, Smith added a two-out solo home run to extend the lead to 3-1. Yolmer Sanchez's RBI double in the fifth and Smith's run-scoring single in the sixth stretched Chicago's lead to 5-1.

In the seventh inning, Chicago added three runs on Garcia's RBI double and a two-run error by third baseman Cheslor Cuthbert.

Winning two of three in the weekend series, the White Sox took the season series 10-9 -- their first season series victory over Kansas City since 2010.

"Everybody is grinding and hustling the way they are supposed to do," Garcia said. "That's big for the team. This team is going to be interesting for the future, so I can't wait for that."

NOTES: Chicago White Sox 1B Jose Abreu (shin) got the day off for rest Sunday after getting his 100th RBI of the season Saturday. He has at least 100 RBIs in four consecutive seasons. Manager Rick Renteria said Abreu would get at least one day of rest. ... White Sox SS Tim Anderson extended his career-high hitting streak to 15 games with a single in the first inning. It is the longest active streak in the majors. ... The Kansas City Royals will play their final road game of the season Monday against the New York Yankees to make up a May 25 rainout. ... Royals 2B Whit Merrifield tops the American League with 33 steals in 38 attempts for 86.8 percent. The last Kansas City player to lead the league in stolen bases was Johnny Damon (46) in 2000.