Yankees right-hander Jameson Taillon (14-5) allowed two runs and seven hits in 7 1/3 innings.
Brian Anderson had three hits and scored two runs for the Marlins, and Jacob Stallings hit a two-run single.
Casas, who finished 3-for-4, clobbered a two-run homer in the second inning.
Hunter Dozier hit a two-run homer for the Royals, who got two hits from Michael A. Taylor.
Altuve went 3-for-4 with four runs, and Hensley contributed an RBI single and a two-run homer.