The defeat pushes the Blue Jays 2 1/2 games behind the Red Sox for first place in the American League East, pending the outcome of Boston's game against the Orioles. Toronto still holds first place in the AL Wild Card standings.
Rays starter Drew Smyly improved to 4-0 lifetime at Rogers Centre, pitching 5 2/3 innings of two-run ball. Smyly's only blemish was a two-run home run to Russell Martin in the bottom of the sixth inning.
Stroman took the loss after allowing three runs over six innings of work. The 25-year-old right-hander battled his command all night, walking four batters for the first time since June 26.