Stepan scored in the final minute of regulation to tie the game and in the final minute of overtime to lift the Rangers to a 4-3 win against the Columbus Blue Jackets at Madison Square Garden.
He scored the winner from below the left circle with 49.6 seconds remaining in overtime. He tied the game with 27.5 seconds remaining in regulation.
New York (51-21-7) will clinch the Presidents' Trophy with a win against the New Jersey Devils at Prudential Center on Tuesday. It needs one point to lock up first place in the Eastern Conference.
The Rangers haven't won the Presidents' Trophy since 1993-94, which was the last time they won the Stanley Cup.
"It's really cool; it's special," Stepan said. "You work hard all season long, you want to be the best. But at the same time there's a lot on our agenda that comes after the Presidents' Trophy that is more on guys' minds. We're trying to get ourselves better to play playoff hockey."
They took another step in the right direction Monday by showing resiliency in the third period after Blue Jackets forward Brandon Dubinsky scored the go-ahead goal at 8:14.
The Rangers killed a penalty on defenseman Matt Hunwick 21 seconds after Dubinsky's goal, and outshot Columbus 9-0 in the final 7:28 of regulation. They had a 6-2 edge in shots on goal in overtime.
"Obviously we never give up," Rangers captain Ryan McDonagh said. "You try to just get something down toward the net and take it into overtime, and let [Stepan] do the rest."
Blue Jackets goalie Sergei Bobrovsky (38 saves) made his best save of the night with 57 seconds left in regulation, when he robbed Rangers defenseman Dan Girardi with a sprawling pad save on an open shot from inches in front of the top of the crease.
Vigneault used his timeout following that save by Bobrovsky. Stepan scored with a one-timer from the lower left circle less than 30 seconds later off a forehanded pass from Chris Kreider, who was in front of the net with his back to Bobrovsky.
"Chris makes an excellent play," Stepan said. "He gets the puck in the throat or the chest and he was able settle it down. To have the sense to know that I'm there is a big time hockey IQ play."
Stepan scored the overtime winner from a similar spot on the opposite end of the ice, but created the chance by forcing a turnover by Blue Jackets defenseman Dalton Prout with a strong stick check along the left-wing half wall.
Bobrovsky saved Keith Yandle's shot from the point, but Kreider tied up Columbus defenseman Justin Falk in front of the crease, allowing Stepan room to collect the puck and time to skate with it, make a forehand to backhand move before beating Bobrovsky on the glove side.
"He's such a good defensive player with his stick there," McDonagh said of Stepan. "Playing against him in practice, it's tough to get that puck by him. He's got a nose for knocking it down and gets his head up right away to make something happen with it. A heck of a game by him all the way from start to finish."
The Blue Jackets (39-35-5) had their club record nine-game winning streak come to an end. They hadn't lost since March 15. They also had their franchise-best eight-game road winning streak come to an end.
"I don't know if it's because we won nine in a row or how we lost this game with a lead in New York, I'm not sure, but whenever you lose it's disappointing and you could tell it still means a lot to the guys in the room," Blue Jackets coach Todd Richards said. "We had our chances to win and it was disappointing. We had some good looks and their goalie made the saves."
Lundqvist didn't get much help as the Rangers were turnover-prone and lackluster on the back check, but stopped defenseman Cody Goloubef and center Ryan Johansen on breakaways when the Rangers were still leading 2-1.
"I think the timing is right there and this game was a good test for me because they have really good quality in their forwards," said Lundqvist, who has won four straight starts. "They move the puck really well. They're able to create some big chances, but over 60 minutes I thought we were the better team. We really earned this one."
Girardi gave the Rangers the 2-1 lead with his fourth goal of the season at 36 seconds of the second period. It came off a strong cycle play by J.T. Miller and Kreider and a crisp circle-to-circle pass from Stepan.
Blue Jackets forward Matt Calvert tied the game at 1-1 late in the first by converting for his 12th goal of the season off a defensive zone turnover by McDonagh. Martin St. Louis got a fortunate bounce off a rush with center Kevin Hayes to give the Rangers a 1-0 lead at 5:38 of the first.
"It comes down to making big plays at the right time and we did," Lundqvist said.
The Rangers have been doing that all season. They're two points away from their first reward, being crowned the best team in the regular season.
"For us to have success in the playoffs we need to up our game," Lundqvist said. "All that matters in the end is what we do in the playoffs."
Follow Dan Rosen on Twitter at: @drosennhl