With the score tied 2-2 in the in the ninth, Getz lifted a one-out double to center field against Darren Oliver (0-1) and Gordon followed with a ground single to right.
Right fielder Emilio Bonifacio's throw was well up the third base line, allowing Getz to cruise home with the game-winning run.
The hit made a winner of Kelvin Herrera (1-0), who tossed a scoreless top of the ninth in relief of starter Ervin Santana.
Lorenzo Cain finished 2-for-4 with an RBI for the Royals, who avoided a three-game home sweep.
Edwin Encarnacion smacked a two-run homer for the Blue Jays.