The Blue Jays concluded the campaign with three consecutive victories and wound up with a winning home record despite an overall mark that was 16 games below the .500 mark.
Minnesota dropped its last five games and its 96 losses were the most in the American League.
Morrow (10-7) gave up three hits and walked one while throwing 110 pitches. Brandon Lyon, who made 67 relief appearances for Houston and Toronto this year, worked the ninth for his first and only save of the season.
Toronto's runs came in the third inning on RBI singles by Rajai Davis and Adeiny Hechavarria.
The loss went to Scott Diamond (12-9), who allowed two runs on five hits in five innings.
2014: The Year in Music [PHOTOS]