Chen (11-7) gave up only two hits while fanning eight and walking one. Louis Coleman came on in the ninth to close out the win for the Royals.
"We played really well. My team played really good defense behind me," Chen said. Salvador [Perez] called a really good game and I felt like I had thrown all my pitches. I felt like I was commanding the baseball."
Carl Pavano (8-12) was tagged with the loss after giving up four runs -- three earned -- on 11 hits while striking out five and walking one over seven innings.
"There's just a lot of things this year throughout the team that we didn't do very well, that we've done well in the past," Pavano said. "That's why we've won and this is why we're losing. What are you going to do? It's not fun at all."
The Royals opened the scoring in the second inning when Moustakas rocketed a one-out homer over the wall in dead center field.
Kansas City added two more runs in the third. Gordon led off the frame by cracking a homer to center field. Cabrera doubled and Billy Butler walked to put runners on second and third with no outs. Eric Hosmer then grounded into a fielder's choice, allowing Cabrera to score.
The Royals added another run in the fourth. Perez whacked a one-out single and moved to second on a wild pitch by Pavano. Perez then hustled home on a single to right by Gordon to account for the final margin.
Minnesota was unable to mount any offense against Chen, getting only one runner to second base, and that took place in the first inning. The Twins were shut out for the 13th time this season.
Chen has a 7-2 career mark against the AL Central and is 1-1 in three starts this season against the Twins...Minnesota leads the season series with KC by an 8-6 count...It was Mauer's 17th start at first base...It was Moustakas' second career major league home run...Minnesota is 29-46 on the road...It was Gordon's 22nd home run of the season.