Chen (6-6) allowed five hits and two walks while striking out six over 5 1/3 innings. Both walks and two of the hits came in the sixth when Houston scored its run.
The Royals fashioned a 2-0 lead before that off Houston starter Jordan Lyles (1-4). Lyles gave up just three hits and didn't walk a batter in a seven-inning outing but still lost.
Lyles retired 12 of the first 13 batters he faced until Mike Moustakas led off the fifth with a double. Moustakas took third on one groundout and scored on one by Brayan Pena.
Houston got two hits off Kansas City closer Jonathan Broxton in the ninth, putting the tying run on third before Broxton got the final outs for his 18th save.