The Blue Jays have captured 10 out of 12 and their winning streak is their longest since they captured 10 in a row in 2008.
Toronto's latest victory came after the Blue Jays fell behind by two in the late innings.
Munenori Kawasaki hit a two-run homer that lifted Toronto into a 6-6 tie in the seventh and the Blue Jays won it in dramatic fashion in the ninth.
Pedro Strop came out of the bull pen to face Davis, who sent a 1-1 pitch into left field to bring home the winning run.
Casey Janssen (2-0) needed just seven pitches to get through the top of the ninth and picked up the win.
Baltimore took a 5-3 lead with a four-run sixth that included a three-run homer by Chris Davis. It was the 27th of the season for Davis, six more than any other player in the majors.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'