The AL East-leading Blue Jays (28-22), who won for the 10th time in 12 games, haven't been atop the division this late into the season since July 6, 2000, when they were 46-40.
Dickey (5-4) allowed one run and five hits in a season-high 8 1-3 innings. He walked one and struck out four.
Jose Reyes and Anthony Gose each scored two runs as Toronto used its speed to hand AL West-leading Oakland its third straight loss, matching its longest slump of the season.
Lawrie's solo homer in the fifth was Toronto's ML-leading 69th, and marked the seventh straight game that at least one Blue Jays batter has connected. Toronto also leads baseball with 37 homers in May.
Dickey retired Derek Norris to begin the ninth, but left after walking Josh Donaldson and giving up a single to Brandon Moss. Yoenis Cespedes singled off Dustin McGowan to load the bases before pinch-hitter Jed Lowrie hit a sacrifice fly off Brett Cecil. Cecil finished it by striking out Alberto Callaspo to earn his third save in four chances.
Oakland opened the scoring when Cespedes hit a one-out homer off Dickey in the second.
Toronto tied it on an unearned run in the third. Gose reached on a fielder's choice and was running from first on Melky Cabrera's two-out single that rolled through the infield after shortstop Eric Sogard broke to cover second base. When left fielder Craig Gentry bobbled the ball, Gose sped around third and slid home under a high throw from Gentry.
Lawrie put the Blue Jays in front with a leadoff homer in the fifth, and Toronto tacked on two more thanks to another Oakland error. Gose and Reyes hit back-to-back singles, and a wild pitch gave the Blue Jays runners at second and third. Cabrera hit a slow roller up the first base line but Moss bobbled the ball, then threw wildly to pitcher Jesse Chavez covering as both runners scored.
Chavez (4-2) allowed four runs, two earned, and eight hits in 5 1-3 innings, the second straight start he has failed to reach six innings. He walked one and struck out four.
Reyes made it 5-1 by scoring from second base on Cabrera's grounder to shortstop in the eight, sliding in ahead of the throw from Moss.
NOTES: The Athletics also lost three straight from April 21-23 and again from May 5-7. ... Oakland C John Jaso (back) missed his second straight game, and manager Bob Melvin said Jaso likely won't play until Monday. ... Athletics INF Nick Punto (left calf) was unavailable. ... Toronto outrighted RH Esmil Rogers to Triple-A Buffalo. ... The roof at Rogers Centre was open for the first time this season. ... Athletics LHP Drew Pomeranz (4-1) faces Toronto LHP J.A. Happ (3-1) in Sunday's series finale.