Blackley (3-2) held the Blue Jays to five hits, one walk, and a solo home run by Travis Snider over seven innings. He won his third decision in a row over.
Toronto starter Brett Cecil (2-3) held the A's to five hits, two walks and two runs, both on a home run by Derek Norris, while striking out a season-best eight in six innings.
But Oakland scored five runs in the seventh against Chad Beck and J.A. Happ to improve their lead to six runs.
Oakland's previous five wins — including a four-game sweep of the New York Yankees — had been by one run and they improved their record in July to 15-2.
The Blue Jays (48-48) had their three-game winning streak end.
J.P. Arencibia hit his 16th homer of the season for the Blue Jays in the ninth against Jim Miller to go 2-for-4 on the game while Brett Lawrie of Langley, B.C., chipped in with three hits for Toronto.
Oakland (52-44) took a 2-0 lead in the second. Cecil retired his first five batters in the game before allowing a single to Brandon Inge and on the next pitch Norris hit his third homer of the season.
It was the eighth home run allowed by Cecil in seven starts since his recall from the minors.
Snider got one back for the Blue Jays with his second homer of the season to lead off the third. Snider was recalled from triple-A Las Vegas on Friday and also homered in Sunday's 15-7 victory at Boston.
Blackley had not allowed a home run in his previous eight games.
Pitchers controlled the game until the seventh when Brandon Hicks doubled against Beck with two out and Jemile Weeks followed with a triple.
Happ allowed a double to Coco Crisp. He walked the next two batters to load the bases for Cespedes who singled to the left-field gap to clear the bases and extend Oakland's lead to 7-1.
Notes: Attendance at Rogers Centre was 25,686..... Reliever Sergio Santos had shoulder surgery on Tuesday. He has been on the disabled list since April 21 with what was listed as shoulder inflammation. The club is not expected to reveal the results of the surgery until Wednesday. ...Reliever Jason Frasor, who was put on the disabled list on Saturday with tightness in his right forearm, had an MRI that revealed only inflammation. He will not throw for two weeks. ...Brandon Morrow is scheduled to throw batting practice on Wednesday in Dunedin, Fla., and if it goes well is expected to begin his rehabilitation assignment on Sunday. He suffered a strained left oblique muscle in his start on June 11. ...Left-hander Ricky Romero (8-6, 5.22 earned-run average), who is 0-5 with an 8.33 ERA in his past five starts, will start for Toronto on Wednesday against Oakland's A.J. Griffin (2-0, 2.70 ERA).