Jason Spezza found the net in the tie-breaker's second round, as did Buffalo's Brad Boyes. But Sabres goalie Jhonas Enroth shut the door the rest of the way, and Roy finally ended it by putting a shot past Curtis Anderson in the sixth round.
Roy also scored in regulation time, as did Jordan Leopold.
Enroth finished with 25 saves for Buffalo, which won for a fifth straight time in Ottawa.
Milan Michalek and Erik Condra found the net for the streaky Senators, who dropped their third straight following a six-game winning streak.
Anderson ended with 31 saves for the Senators.