Gose's two-run single highlighted a five-run second inning that broke the game open for the Blue Jays, who clinched their three-game series.
Toronto outfielder added a three-run homer in the ninth to cap the scoring after the contest had been delayed twice by rain.
Yunel Escobar also went deep to aid Toronto's victory.
Brad Lincoln (1-0) was credited with the win after the delays interrupted starter Aaron Laffey, who had allowed two runs on four hits over 4 2/3 innings.
Red Sox starter Daisuke Matsuzaka (1-5) was pounded for five runs on five hits while lasting just 1 1/3 innings.
Pedro Ciriaco and Scott Podsednik drove in runs for the Bosox.