CHICAGO — The Royals jumped on the White Sox early in Sunday’s finale at Guaranteed Rate Field, piling on six runs in the second inning.

Ryan O’Hearn, Whit Merrifield and Alex Gordon all went deep in the inning, the Royals’ third-biggest inning of the season. And despite Kansas City ultimately falling to Chicago, 7-6, the inning illustrated some positive signs for a slumping Royals offense.

“I liked the fact that Whit and Gordon were swinging the bat well,” manager Ned Yost said. “[Jorge Bonifacio] with three hits today. O’Hearn’s a positive too.”

Over their past six contests, the Royals have averaged 5.17 runs per game, well above their season-long 3.68 per game average that ranked last in the Majors entering Sunday. O’Hearn especially is beginning to make his mark as the rookie, who made his MLB debut July 31, hit his fourth homer in his first 42 plate appearances.

O’Hearn’s slugging percentage now stands at .514 (37 at-bats) after Sunday. Although O’Hearn’s last Minor League homer came on July 2, he said he hasn’t changed his approach at the plate.

“That’s just how the game works, just go up there and hit the ball hard,” O’Hearn said. “I feel real comfortable, wish I had a little bit more production against left-handed pitching, but that’s something that I think will come around as time goes on.”

Heath Fillmyer started strong, striking out the first batter he faced, and he got through the first three innings without issue and retired eight straight White Sox hitters at one point. But Chicago jumped all over Fillmyer in the fourth, opening the inning with seven straight hits.

Fillmyer was charged with all six runs in that fourth, as the White Sox answered Kansas City’s three homers with three of their own. Avisail Garcia, Tim Anderson and Omar Narvaez were the culprits.

“I tried to just hit the reset button after every pitch, but the pitches just weren’t in the spots where I needed them to be,” Fillmyer said. “Some of them hit good pitches and some of them hit the pitches they were looking for, so it’s just lack of execution. I need to be better.”

“He just couldn’t stop the bleeding,” Yost said of Fillmyer. “Second time around they got on him. Wasn’t a bad pitch to Garcia, but from that point on it just snowballed on him.”

Chicago tacked on a run in the fifth on a Narvaez RBI single, and though the Royals’ bullpen turned in another strong performance — they’ve now given up just one run in their last 10 2/3 innings — the offense stalled after the big second inning.

“Funny how we hit three homers, they hit three homers,” Yost said. “We scored six, they scored six. But the fifth inning, when they scored the winning run, was a nice piece of hitting by Narvaez the opposite way.”