The Senators' victory filled out the list of playoff teams in the Eastern Conference. The New York Rangers had claimed a post-season spot minutes earlier with an overtime decision over Carolina.
The wins by Ottawa and the Rangers eliminated Winnipeg from playoff contention even as the Jets were battling Montreal in their final game of the season.
Ottawa, the Rangers and the New York Islanders are tied for sixth place in the East at 54 points with one game remaining.
Jakob Silfverberg opened the scoring for the Senators on a tip-in with 7:25 to go in the first period, but Alex Ovechkin tied it with his NHL-leading 32nd of the season midway through the third.
That was all the scoring until Gonchar beat Michal Neuvirth with Mike Ribeiro in the penalty box for roughing.
Craig Anderson made 19 saves in the big win while Neuvirth stopped 39-of-41 shots.