"We put together a good game," Blue Jays manager John Farrell said. "We were able to exploit the speed that both guys have at the top.
Tommy Milone (9-9) lost his third straight start and is 1-3 in his last seven.
"Something is just a little off in my delivery and the ball is sailing up in the zone," Milone said. "I couldn't get that one pitch I needed."
Aaron Laffey (3-2) won for the third time in four decisions after allowing four runs on six hits over six innings. He walked one and struck out four.
Casey Janssen pitched the ninth for his 14th consecutive save.
Toronto had its best offensive output in 10 games. The Blue Jays averaged just under two runs a game in their previous eight.
Rajai Davis scored from second base on a sacrifice bunt from Gose to put the Blue Jays ahead in the first. David doubled to open the game and was already at third base by the time Norris was just getting rid of the ball from Gose's bunt.
"I wish I could say we practiced that, but we didn't," Gose said. "Rajai was on the move and I should have taken the pitch and let him steal a base, but I put the bunt down and heads up baserunning made things happen."
Norris' double in the second scored Brandon Inge with the tying run, and Reddick's three-run drive into the right-field bleachers put the A's ahead 4-1 in the third.
"A couple of plays here and there cost us," A's manager Bob Melvin said.
Encarnacion's 29th home run closed the gap to 4-3 in the fourth, and Toronto took the lead in the fifth when five hitters reached with two outs. Escobar's two-run single and Johnson's RBI single were the key hits.
"We have been struggling the past couple of games," Encarnacion said. "That homer gave everybody a little more emotion and everybody started hitting better."
Adam Rosales doubled with one out in the seventh and scored on Crisp's double to make it 6-5.
A's RHP A.J. Griffin went on the DL with a strained right shoulder. ... Oakland OF Michael Taylor was optioned to Triple-A. ... The A's recalled left-hander Pedro Figueroa and right-hander Evan Scribner from Sacramento. ... Blue Jays RHP Carlos Villanueva left the team for personal reasons. Toronto RHP Jesse Chavez was optioned to Triple-A. ... LHP J.A. Happ will move up to start Tuesday's game for the Blue Jays. ... Toronto also selected RHP Chad Jenkins from Double-A New Hampshire. ... The A's are 14-6 in one-run games at home.