Hall came down the right side on the first possession of the extra frame and fired a shot that was stopped by Craig Anderson.
Shawn Horcoff's follow-up was also turned aside by the Senators' goalie, but Hall, who had come around from in back of the net, backhanded home the Oilers' third try for the game-winner.
Magnus Paajarvi added a goal and an assist while Horcoff and Ben Eager also found the net for Edmonton, which broke an eight-game losing streak in Ottawa.
Nikolai Khabibulin turned aside 39-of-42 shots to earn the win.
Anderson finished with 36 saves for the Senators, who lost for the fourth time in five home games.