De La Rosa held the Twins to no earned runs and five hits while throwing a career-high eight innings. He retired 16 straight during one stretch to help the Royals win a series for the first time this season.
Ross Gload put the Royals ahead to stay with a two-run homer in the third inning. Mike Sweeney went 3-for-4 with an R-B-I single to support De La Rosa's second victory in three decisions.
Ortiz was reached for three runs and seven hits in seven innings to fall to 3-and-1.
Michael Cuddyer (kuh-DY'-ur) doubled home the Twins' lone run in the sixth.