Punto doubled home a run and scored on Daniel Nava's two-run single to highlight a decisive four-run second inning and added a solo homer in the ninth for the Red Sox.
Will Middlebrooks and Ryan Sweeney also provided RBI as Boston clinched its three-game set at Rogers Center.
Doubront (6-2) yielded two earned runs on seven hits over 6 1/3 innings, striking out seven while walking only one to earn his fifth victory in six starts.
Alfredo Aceves picked up his 14th save with a 1-2-3 ninth inning.
Toronto's Kyle Drabek (4-6) absorbed the loss, allowing five runs (four earned) on six hits in a 6 2/3-inning stint.