The Senators’ 3-1 victory over Philadelphia capped a 23-4-4 run to end the season and lay an 11th-hour claim on an Eastern playoff slot.
Ottawa, who were one of the league’s bottom dwellers just two months ago, will visit Montreal when the first round begins on Wednesday, after the Canadiens clinched first place in the Atlantic Division with a 4-3 shootout win over Toronto.
The Penguins defeated Buffalo 2-0 and will now face the President’s Trophy-winning New York Rangers in the playoffs.
Pittsburgh’s win, combined with Boston’s 3-2 defeat to Tampa Bay means the Bruins will miss the post-season for the first time since 2007.
The Lightning will host Detroit in the opening game of their best-of-seven first-round series.
The other Eastern showdown will see the Washington Capitals host the New York Islanders, who failed to clinch second in the Metropolitan Division following their 5-4 shootout loss to Columbus.
In the Western Conference, Anaheim claimed top seed with a 2-1 win over Arizona and will host the Winnipeg Jets, who are making their first playoff appearance since moving from Atlanta in 2011.
Meanwhile, Vancouver will host Calgary in their opener, St Louis will face Minnesota, and Nashville will have home advantage first against Chicago.
Philadelphia 1-3 Ottawa
Washington 2-4 NY Rangers
Winnipeg 5-1 Calgary
Los Angeles 4-1 San Jose
St Louis 4-2 Minnesota
Buffalo 0-2 Pittsburgh
Toronto 3-4 Montreal (SO)
Florida 3-2 New Jersey
NY Islanders 4-5 Columbus (SO)
Carloina 0-2 Detroit
Tampa Bay 3-2 Boston (SO)
Dallas 4-1 Nashville
Colorado 3-2 Chicago
Arizona 1-2 Anaheim
Vancouver 6-5 Edmonton