Derek Holland, who won 16 games for the Rangers last season, allowed one run and three hits over two innings in his first spring start.
Alex Gordon hit a two-run homer to trim Texas' lead to 6-3 in the fifth. Derrick Robinson added a two-out, two run single in the sixth, and pinch-hitter Kevin Kouzmanoff delivered a two-run double with two out in the ninth to give the Royals the victory.
Kansas City left-hander Bruce Chen gave up five runs and seven hits in 1 2-3 innings. One run was unearned after second baseman Johnny Giavotella's throwing error.