The New York Rangers set a franchise record, won the Eastern Conference title and also a Presidents’ Trophy that comes with mixed blessings.

Igor Shesterkin made 26 saves to beat the Ottawa Senators 4-0 in New York's season finale and give the Rangers a 55-23-4 record and franchise-best 114 points.

The Rangers clinched their fourth Presidents' Trophy (top regular-season record) in franchise history, which guarantees them home-ice advantage through the playoffs. But it also comes with a postseason jinx.

The last Presidents' Trophy winner to also win a Stanley Cup title was the 2012-13 Chicago Blackhawks. Last season's winner, the record-setting Boston Bruins, were upset in the first round by the Florida Panthers.

Only eight teams have won the regular-season title and Stanley Cup in the same year. The Rangers did it in 1994 after having a league-best 112 points. They lost in the conference finals during their 113-point season of 2014-15, the record that the current team broke on Monday night.

Islanders clinch playoff spot

The New York Islanders downed the New Jersey Devils 4-1 to clinch both a playoff spot and the third seed in the Metropolitan Division. They’ll face the No. 2 Carolina Hurricanes in the first round.

Coach Patrick Roy, who returned to the NHL after a long absence as a midseason replacement for fired Lane Lambert, made the playoffs for the first time since 2013-14 with the Colorado Avalanche. The Hall of Fame goaltender won four Stanley Cup titles as a player.

Roy has gone 19-12-5 and the Islanders are on a 7-0-1 run.

"We played some very good hockey down the stretch and they were resilient," Roy told reporters. "They worked together. I think we learned how to win."

Capitals, Red Wings, Penguins all win: What that means

The Detroit Red Wings' 5-4 overtime win was the most dramatic because they trailed the Montreal Canadiens 4-2 in the third period. Detroit's Lucas Raymond tied the game with 1:17 left and scored at 4:35 of overtime.

The Capitals beat the Boston Bruins 2-0 and the Pittsburgh Penguins defeated the Nashville Predators 4-2.

All three teams are still alive in the battle for the final playoff berth, the second wild-card spot in the Eastern Conference. So are the idle Philadelphia Flyers.

The Capitals will clinch the berth if they beat the Flyers in Philadelphia on Tuesday.

The Red Wings clinch if they win in Montreal on Tuesday and the Flyers beat the Capitals.

The Flyers clinch if they beat the Capitals in regulation, the Red Wings lose in regulation and the Penguins lose to the Islanders in regulation on Wednesday.

The Penguins will clinch if they beat the Islanders and the Capitals and Red Wings lose in regulation.

Connor McDavid hits rare milestone as Oilers stay alive in division race

Edmonton Oilers star Connor McDavid became just the fourth player in NHL history to record 100 assists in a season. He joined Wayne Gretzky (11 times) and Mario Lemieux and Bobby Orr (once each) when he set up Zach Hyman's goal in the 9-2 victory.

The win kept alive the Oilers' long-shot chance of winning the Pacific Division. The Vancouver Canucks hold a three-point lead and each team has two games left.

Bruins miss chance to clinch Atlantic Division title

The loss to the Capitals kept them one point ahead of the Florida Panthers. The Bruins have another chance Tuesday against the Senators. If they lose and the Panthers beat the Toronto Maple Leafs, Florida clinches the title.

Kings lose: What that means

The Kings are at 97 points after falling to the Minnesota Wild and have one game left, against the Chicago Blackhawks. That means the Vegas Golden Knights (96) can move up to the third spot in the Pacific Division if they win their final games against the Blackhawks and Anaheim Ducks.