Rasmus also doubled off his younger brother, Braves reliever Cory Rasmus, but Toronto lost third baseman Brett Lawrie to a sprained ankle.
Encarnacion went 2 for 5 with five RBIs as the Blue Jays improved to 3-0 in interleague play. Toronto has won nine of 12 against NL opponents dating to last season.
Mark Buehrle (2-3) allowed one run and five hits in six innings to snap a seven-start winless streak and earn his 26th career interleague victory. The veteran left-hander, whose previous win was April 15, is the all-time leader in interleague wins.
Buehrle walked two and struck out six. He retired 11 of his first 13 batters and didn’t allow a hit until Evan Gattis’ two-out double in the fourth.
Brad Lincoln worked two innings and Thad Webber finished for the Blue Jays.
Lawrie left in the sixth after spraining his left ankle sliding into second on a stolen base. He initially stayed in the game but was visibly hobbled advancing to third on Emilio Bonifacio’s grounder. Mark DeRosa came on to pinch run, then replaced Lawrie at third base.
The Blue Jays said he is day to day.
Gattis hit his 11th homer, a two-run shot off Lincoln in the eighth, but the Braves lost their second straight following an eight-game winning streak.
Tim Hudson (4-4) matched a season worst by allowing six runs and eight hits in six innings, extending his winless streak to four starts.
Adam Lind doubled leading off the second and, one out later, Colby Rasmus hit his eighth homer into the second deck.
Toronto added two more in the third. Melky Cabrera walked, Jose Bautista doubled and both runners scored on Encarnacion’s single.
Buehrle’s shutout bid ended in the fifth when Chris Johnson doubled and scored on a two-out single by Andrelton Simmons.
After Lind walked to begin the sixth, Arencibia followed with a shot to center, his 12th.
Toronto put it away in the seventh against Cory Rasmus. Cabrera doubled, Bautista walked and Encarnacion hit a first-pitch homer, his team-high 14th.
Two batters later, Colby Rasmus doubled off his brother, the first time they had faced each other in the majors.
It was the first time brothers had gone head-to-head in a big league game since June 13, 2010, when pitchers Jered and Jeff Weaver squared off in an interleague meeting between the Los Angeles Angels and Dodgers.