The Capitals, Columbus Blue Jackets and Chicago Blackhawks already have clinched playoff berths.
On Monday, the Toronto Maple Leafs solidified their hold on a playoff spot with a 4-2 win against the Bruins.
The Maple Leafs, who swept the four-game season series against the Bruins, are three points ahead of the New York Islanders for the second wild card into the playoffs from the Eastern Conference. Each team has played 71 games.
Toronto also moved one point behind Boston for third place in the Atlantic Division. Boston has 82 points but has played one more game. The Senators, who have a game in hand, have a four-point lead on the Bruins for second place in the division.
If the season ended today, Boston would face Ottawa in the playoffs, while the Maple Leafs would play the Capitals.
The Tampa Bay Lightning, who host the Arizona Coyotes on Tuesday (7:30 p.m. ET; TVA Sports, SUN, FS-A PLUS, NHL.TV), can leapfrog the Islanders in the wild-card chase with a win.
There was some movement in the Western Conference on Monday.
With a 3-1 victory against the Coyotes, the Nashville Predators moved into third place in the Central Division, knocking the idle St. Louis Blues into the second wild card spot.
The Blues, two points behind the Predators, visit the Colorado Avalanche on Tuesday (9 p.m. ET; ALT, FS-W, NHL.TV) and can reclaim third place with a victory. If the Blues win, each team would have 83 points, but the Blues would hold the regulation-plus-overtime wins (ROW) tiebreaker (38-34).