Mika Zibanejad scored two goals to reach 20 this season and added an assist. Chris Kreider had a goal and an assist, and Vincent Trocheck scored.
The Rangers (39-36-7) are not going to the Stanley Cup Playoffs after winning the Presidents’ Trophy last season. They were eliminated from playoff contention on April 12.
Jonas Johansson made 19 saves for Tampa Bay, which lost in regulation for the second time in 12 games since March 25 (7-2-3).
The Lightning (47-27-8) will play the Florida Panthers in the Eastern Conference First Round. Game 1 is at Amalie Arena on Tuesday.
Trocheck put the Rangers ahead 1-0 with a short-handed goal at 1:02 of the second period off a give-and-go with J.T. Miller.
Trocheck got the puck at the right point off a Lightning defensive zone turnover. He chipped it around Nikita Kucherov and took it into the right face-off circle, found Miller in the high slot and immediately got the puck back to score glove side from low in the circle.
It was Trocheck’s fourth short-handed goal in the past nine games. The Rangers finished with a League-high 18 short-handed goals. Trocheck accounted for six, tied for the NHL lead with Buffalo Sabres forward Alex Tuch.
Kreider made it 2-0 at 4:02 of the third period, scoring with a shot over Johansson’s glove from between the circles after his initial shot was blocked by Yanni Gourde.
Zibanejad scored with a one-timer from the left circle to make it 3-0 at 12:50. He added another at 16:24, getting a piece of Kreider’s shot from the right boards for the 4-0 final.