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 in 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.
"I feel like I've been right on the edge of a game like this for a long time," Dickey said.
Dickey lowered his ERA to 3.95. It's the first time since joining Toronto before the 2013 season that he had an ERA below 4.00
"He was dealing, he was strong, he was very efficient," Blue Jays manager John Gibbons said.
Oakland's Craig Gentry, who went hitless in three at bats, found it a frustrating afternoon against Dickey's dancing pitch.
"It was moving all over the place and we just couldn't get anything going against him," Gentry said.
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.
"We're playing good baseball," Reyes said. "It's always fun when you're winning."
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.
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.
"I just came in too hard," Gentry said. "I should have been a little more under control. I was just being too aggressive."
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.
"The guys were commenting that the ball was a little bouncier than normal," Oakland manager Bob Melvin said. "That's typical with Astroturf when the sun is out. We hadn't played in those conditions yet."
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.
"You know the old saying that speed never goes in slumps," Gibbons said. "It can make things happen."
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. ... Athletics INF Nick Punto (left calf) was unavailable. ... Toronto outrighted RH Esmil Rogers to Triple-A Buffalo. ... Oakland dropped to 19-3 when scoring first. ... 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.
Copyright by STATS LLC and The Associated Press
TORONTO, CANADA - MAY 24: R.A. Dickey #43 of the Toronto Blue Jays delivers a pitch in the first inning during MLB...
29,372 (59.6% full) - % is based on regular season capacity
61 degrees, sunny
Home Plate - Will Little, First Base - Mark Carlson, Second Base - Ted Barrett, Third Base - Paul Schrieber
Opposing hitters are hitting .156 against Jesse Chavez' changeup this year, which is 77 points below the league average of .233. Brett Lawrie has a batting average of .182 against changeups this season, which is 61 points worse than the average among qualified hitters.