Venable singled off Tim Collins (0-2) and over the head of right fielder Lorenzo Cain to score Chris Denorfia with the tying run and Yonder Alonso with the winning run from second base.
Denorfia led off the inning with a single off Louis Coleman before Collins came on. After a sacrifice, Alonso reached a bloop double to left to bring up Venable.
Mike Moustakas hit an RBI single in the 12th off Tim Stauffer (1-0) to give the Royals a brief lead.
Jedd Gyorko’s solo homer with one out in the ninth inning off Royals closer Greg Holland tied the game at 4. It was Holland’s first blown save in eight chances.