Finnegan looked dominant in his first inning, getting the White Sox 4-5-6 hitters -- Alexei Ramirez, J.B. Shuck and Gordon Beckham -- on three easy outs in the fifth.
"It felt good," he said. "You just want to get your work in. It's the first little competitive outing I've had all Spring Training."
Finnegan got nicked for two runs in the sixth inning, though the inning was Arizona-tainted -- the White Sox got an infield hit, a seeing-eye grounder for a hit, and a slicer to left for a hit.
"They got a couple of hits," Finnegan said. "That's going to happen.
"But I felt pretty good out there. For the first time out there, it felt fine."
Royals manager Ned Yost thought Finnegan had a solid outing.
"He had a real good first inning," Yost said. "All in all, just a good first outing."
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @jflanagankc. This story was not subject to the approval of Major League Baseball or its clubs.