The Blue Jays were trailing 2-1 entering the eighth when they began a comeback, with pinch-hitter Munenori Kawasaki and Jose Reyes (3-for-4) delivering singles off Kelvin Herrera (5-7).
Crow came in and issued successive run-scoring walks to Brett Lawrie and Rajai Davis.
R.A. Dickey (11-12) tossed eight innings, yielding two runs on seven hits. The knuckleballer walked two and struck out six as Toronto clinched its three-game series.
Eric Hosmer went 2-for-3 with an RBI for the Royals.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys