David Murphy hit a solo home run and Yan Gomes drove in one for the Indians, who had won six of eight coming in. Danny Salazar (1-4) gave up two runs on five hits over four innings to take the loss.
In the second, Encarnacion led off the frame with his seventh home run of the season, and Francisco added his seventh of the season two batters later for a 2-0 lead.
Cleveland got a run back in the fifth off Murphy's third homer of the season, a solo shot to right.
The Blue Jays, though, answered in the home half off C.C. Lee as Jose Bautista led off with a single and Encarnacion followed with a bomb to left for his eighth of the year and a 4-1 lead.
In the eighth, the Indians trimmed their deficit as Ryan Raburn led off with a ground-rule double and later scored on a Gomes single. Aaron Loup then came on and struck out Murphy to strand two runners.
Casey Janssen tossed a quiet ninth for his second save of the season.
2014: The Year in Music [PHOTOS]