Bautista's sixth-inning blast gave Toronto a 3-0 lead and the Canadian squad hung on to record their third victory in four games.
The Blue Jays found out before the game that Reyes -- who was obtained in a 12-player, off-season trade with Miami -- could miss up to three months after being diagnosed with a sprained left ankle.
The all-star was put on the 15-day disabled list and replaced on the roster by Munenori Kawasaki, who provided a sacrifice fly a run scored in the victory after being recalled from Class AAA Buffalo.
R.A. Dickey (1-2) earned his first victory in a Toronto uniform, allowing one run on five hits over 6 1/3 innings.
Casey Janssen recorded his third save despite yielding a run in the ninth.
Royals starter James Shields (1-2) took the complete-game loss, surrendering three runs on just two hits with six strikeouts.
Chris Getz went 3-for-4 with an RBI for Kansas City.
2014: The Year in Music [PHOTOS]