It was the fifth-consecutive loss for the Twins and the fifth straight win for the Royals, who snapped a seven-game losing streak Sunday.
Chen (6-2) allowed five hits and one walk in 5 2/3 innings. He struck out three. One of the hits he surrendered was Brian Dozier's 14th home run of the season in the sixth inning.
Kelvin Herrera chipped in 1 1/3 innings in relief, Will Smith pitched one inning and Greg Holland came on in the ninth, earning his 36th save as the Kansas City bullpen combined for 2 1/3 innings with no hits, one walk and five strikeouts.
The Royals only had six hits but got half of them in the second inning when they scored all their runs.
Billy Butler led off the inning with a walk off Samuel Deduno (8-8) and Justin Maxwell was hit by a pitch. Both moved up on a fielder's choice before Alcides Escobar singled in Butler and Chris Getz had a base hit to score Maxwell. Alex Gordon had an RBI single to complete the rally.