Billy Butler's RBI groundout in the fourth inning triggered a three-run rally, highlighted when Maier belted a 2-1 pitch into the right-center field gap that just eluded the Tigers' Austin Jackson, scoring Eric Hosmer from first.
Maier then came in to score on Brayan Pena's single and the Royals added a solo homer from Johnny Giavotella in the next frame to avoid a three-game sweep at the hands of the Tigers.
Bruce Chen (6-5) yielded three runs over five innings for the victory while Louis Coleman, Greg Holland and Joakim Soria (21st save) shut Detroit down the rest of the way, securing the win.
Max Scherzer (11-7) was touched for four runs on six hits over five frames for the American League Central-leading Tigers.
Andy Dirks, Jackson and Miguel Cabrera each knocked RBI doubles in the sixth for Detroit.
Swim Week Miami Beach 2014 [PHOTOS]