The win in the opener of a four-game series gave the Blue Jays their third triumph in four contests.
Baltimore took a 3-0 lead in the fourth, but by the end of the sixth inning the Orioles had fallen behind 8-3.
Arencibia doubled home a run for the Blue Jays in the fourth and scored on Emilio Bonifacio's sacrifice fly. Arencibia smashed a two-run homer in the fifth to put the Blue Jays in front and Toronto expanded its lead in the sixth when Encarnacion hit his home run to left.
The third of those walks was issued by Pedro Stump, who then gave up Encarnacion's 13th home run of the season.
Baltimore battled back to within two runs in the eighth, but Toronto added four more in the bottom half of the inning -- Arencibia driving in one of them with a ground out. The four Toronto runs in the eighth came with the help of a walk, an error and a passed ball.
Toronto starter Brandon Morrow (2-3) gave up six runs on 10 hits, but he lasted seven innings and became the winning pitcher thanks to Toronto's big night on offense.
The loss went to Kevin Gausman (0-1), who was roughed up in his major league debut. He gave up four runs on seven hits in five innings with two walks and five strikeouts.