Toronto has won three in a row, one short of its longest winning streak of the season. Baltimore has dropped five straight.
Morrow (6-3) bounced back from a dismal performance against Texas in which he retired only two batters while allowing nine base runners and six runs.
Janssen picked up his fifth save.
Toronto's runs came on solo homers in four consecutive innings beginning in the second. The home runs came from Edwin Encarnacion, Rajai Davis, Brett Lawrie and Colby Rasmus -- all off Jason Hammel (6-2).