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.