CHICAGO — A few days ago, Royals rookie Ryan O’Hearn was still toiling with Triple-A Omaha, still dreaming about when his shot at the big leagues would come.

That shot came two days ago when O’Hearn was informed he would be joining the Royals here. And O’Hearn, 25, didn’t waste much time making the moment matter. In his second at-bat Tuesday, O’Hearn hit a two-run home run — his first big league hit — and the Royals went on to a 4-2 victory over the White Sox at Guaranteed Rate Field.

Left-hander Danny Duffy (7-9) got the win. Wily Peralta picked up his sixth save.

O’Hearn pounced on a 1-0 curveball from former Royals right-hander James Shields in the fifth inning and knocked it over the right-field fence. The homer gave the Royals a 2-0 lead.

“Hitting a homer off James Shields, a guy I’ve watched pitch, it’s a dream come true,” O’Hearn said. “This is the most fun I’ve had in baseball.

“I had mom and dad and brother and sister here. They were right above the dugout. It’s special. It’s going to be really cool in a minute when I can go give them a hug.”

O’Hearn became the third player in team history to homer in his first big league game — Clint Hurdle (1977) and Mark Quinn (1999) were the others.

Royals manager Ned Yost said everyone in the dugout was pumped for O’Hearn.

“We all know what it’s like to work your whole life to get up here, and then to homer in your first game, it is special,” Yost said. “You want to enjoy it with him.”

The Royals also got a lift from another newcomer. Center fielder Brett Phillips, just acquired from Milwaukee in the Mike Moustakas trade Friday night, also jumped on a Shields curveball and ripped a two-run home in the seventh.

“Those two guys really gave us a boost,” Yost said.

Duffy maneuvered through a lot of traffic and provided 5 2/3 innings of scoreless ball. Duffy gave up six hits and walked four.

But Duffy did strike out seven and got some big outs when he needed them. In the fourth, the White Sox loaded the bases with one out, but Duffy got Omar Narvaez to hit into a 5-2 fielder’s choice. Duffy then got Tim Anderson on a flyout.

“He pitched OK,” Yost said. “I thought he had a really good fastball, 94-95 [mph]. Good curveball. His pitch count just got elevated.”