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 his 20th goal of the season and the 4-0 final.
"Kind of empty," Zibanejad said of how he feels now that the season is over. "Coming into the rink this afternoon with the weather being like it is, I'm used to gearing up for playoffs, but that's not the case now."
It is for the Lightning.
"Now it starts," Tampa Bay forward Nick Paul said. "Now our gameplan starts. Fly home tonight, figure out what days we're practicing and what days we're off, and just prepare for a great series. … We know what it takes and every guy in here is ready to buy in."
NOTES: Zibanejad's two goals give him 250 as a Ranger, tying him with Mark Messier for the eighth-most in team history. … It's also Zibanejad's eighth straight 20-goal season, tied for the longest streak in team history with Jean Ratelle. He is the fifth Swedish-born player to have eight straight 20-goal seasons, joining Mats Sundin (17), Daniel Alfredsson (10), Markus Naslund (10) and Mats Naslund (8). … Zibanejad's eight 20-goal seasons are the fourth-most in team history behind Rod Gilbert (12), Kreider (10) and Ratelle (nine).