Powell's grand slam, his fifth homer this season, capped a five-run inning, giving Oakland an 8-0 lead with two outs in the bottom of the second.
Mark Ellis drove in a run.
Winner Trevor Cahill (8-12) gave up three runs and six hits in five innings.
Josh Anderson led Kansas City with two hits and one RBI.
Mike Jacobs, David DeJesus and Alberto Callaspo each had one RBI, with Jacobs hitting a solo homer in the third, his 17th.
The losing pitcher was starter Brian Bannister (7-12).
Swim Week Miami Beach 2014 [PHOTOS]