Andrei Vasilevskiy made 17 saves for the Lightning (21-8-5) in his return after missing three games while in COVID-19 protocol.
"It's not like the guys weren't trying, we just didn't generate anything," Tampa Bay coach Jon Cooper said. "We were just off and give credit to the Rangers. They did a [heck] of a job. We did get chances and the goalie was able to see them. We were a step slow, and our reaction time was a little bit off. When that happens, this is the result."
Zibanejad made it 1-0 with a power-play goal at 7:44 of the first period, beating Vasilevskiy to the near post with a wrist shot from inside the left circle. He extended the lead to 2-0 at 12:37 with another goal on the man-advantage when his shot deflected in off Ryan McDonagh's stick.
"I'm happy to help and as long as we win, it doesn't matter," Zibanejad said. "At the end of the day, I feel like I have that role to produce offense and to produce goals or assists to goals. It's always nice when it goes in and we can help, and it helps the team to win."
Strome made it 3-0 at 14:53 when he scored from the high slot off a pass by Barclay Goodrow.
"All of our players stepped up," New York coach Gerard Gallant said. "The best player was really good today, obviously, but all of our players stepped up."
Zibanejad completed the hat trick to make it 4-0 at 16:53 of the second period, tipping in Kreider's initial shot. The center has eight NHL hat tricks, including seven with the Rangers.
"First one was on the power play, second one deflected off their stick, I think, and third one was a great play by 'Krieds,'" Zibanejad said. "When you have that kind of momentum, you seem to make the right decisions of where to go, and pucks find you."
Shesterkin, who made 25 saves in the win at Tampa Bay on Friday, made nine saves in the third period to preserve his second shutout of the season.
