Roy redirected Chris Drury's shot past goalie Ray Emery after Senators defenceman Andrej Meszaros turned over the puck in Ottawa's zone after the opening faceoff.
Meszaros' pass struck Roy's skate and deflected to Drury inside the blue line. Drury fed a pass to the right of the net where Roy was alone to deflect the puck just under the crossbar.
It was the fastest goal from the start of the game in Sabres playoff history. Henrik Tallinder scored at 33 seconds on May 13, 2006.
Los Angeles' Don Kozak set the NHL record for the fastest goal in a playoff game when he scored six seconds into the Kings' 7-4 win over Boston on April 17, 1977.
Roy's goal, also the fastest allowed by the Senators in a post-season game, ended a Buffalo scoring drought of 85 minutes, 13 seconds that dated to Daniel Briere's overtime-forcing goal with six seconds left in a 4-3 double-overtime loss in Game 2 on Saturday.
Alexander Mogilny scored the fastest goal from the start of a game in Buffalo history when he scored five seconds into a regular-season game against Toronto on Dec. 21, 1991.