Chen (4-0) yielded one run on three hits over six innings. The left-hander didn't allow a walk and struck out four, exiting with a 3-1 lead.
Kelvin Herrera and Aaron Crow each hurled a scoreless relief frame but closer Greg Holland ran into trouble in the ninth.
But that was all the further he got as Holland struck out Chris Davis and retired J.J. Hardy and Henry Urrutia on grounders to end the game and pick up his 25th save.
Mike Moustakis and Chris Getz each drove in a run for the Royals, who rebounded from a 9-2 defeat in Monday's four-game series opener.
Jason Hammel (7-7) was tagged with the loss, surrendering three runs on 10 hits over six full innings.
Manny Machado socked a solo homer for Baltimore.
Celebrity Families of 2014 [PHOTOS]