The Rays won 14 of 18 against the Blue Jays this season.
Crawford's homer, his 14th, gave Tampa Bay a 2-0 lead with no outs in the bottom of the first.
Willy Aybar hit a solo homer, Pat Burrell had three hits and Ben Zobrist and B.J. Upton had two hits apiece for the Rays, who have won four in a row.
Winner David Price (9-7), the first of six Tampa Bay pitchers, gave up a run and just three hits in 6 2/3 innings.
Edwin Encarnacion's fourth-inning homer accounted for the only run for the Blue Jays, who have lost four straight.
Losing pitcher Roy Halladay (15-10) surrendered two runs and 10 hits in seven innings.
Copyright 2009 by United Press International.