COLUMBUS, Ohio -- The New York Rangers breathed a collective sigh of relief Monday night after a 4-2 victory over the Columbus Blue Jackets punched their ticket to the NHL playoffs.

After whiffing in two previous tries to secure a postseason spot, the Rangers asserted themselves in the first two periods and then held off the Blue Jackets in the final period in Nationwide Arena to advance to the playoffs for the sixth consecutive season.

New York (44-26-9) was 0-2-1 in its previous three games and lost to non-playoff qualifiers Carolina and Buffalo in the past week before taking care of the business on the road against Columbus (31-40-8), another opponent that will not be advancing past the regular season.

The Rangers acknowledged afterward that they were feeling some pressure, particularly in the third period after the Blue Jackets closed within 3-2 on Nick Foligno's second goal of the game with 9:15 remaining.

With 2:03 left, Rangers center Mats Zuccarello was called for a high-sticking penalty, and the Blue Jackets applied even more pressure by pulling rookie goaltender Joonas Korpisalo for an extra attacker to make it six-on-four.

However, Rangers center Derek Stepan gained control of the puck in the center of the ice and sent an unassisted, short-handed backhander into the Columbus empty net for his 20th goal of the season with 1:11 remaining to secure the victory.

"Everyone was feeling a little bit of pressure to win a game and get in," Rangers defenseman Marc Staal said. "Not we can focus on the way we're playing going into the playoffs."

Chris Kreider, Dan Boyle and Zuccarello scored goals in the first two periods as the Rangers took a 3-1 lead.

Rangers goaltender Henrik Lundqvist bounced back from a subpar outing in his previous game to make 27 saves Monday. On Saturday, he gave up three goals and was pulled early in the second period of a 4-3 loss to the Sabres.

Lundqvist, who improved his record to 34-20-7, extended his winning streak against Columbus to six games dating to March 2014.

"It hasn't been pretty at times, but playing in this league is a grind," Lundqvist said. "We're in. It's just a really good feeling.

"It was a great feeling to see how we played and how determined we were. We were blocking a lot of shots. We scored at the right times as well. It was a hard-fought game. We knew they were going to play hard."

Hurt by slow starts in the previous four games, the Rangers scored first at 6:17 of the first period. Kreider fired a shot from the left faceoff circle that Korpisalo stopped, but the rebound went right back to Kreider, and his backhander found the net for his 20th goal of the season.

Boyle increased the Rangers' lead to 2-0 at 5:28 of the second period with his ninth goal of the season. His snap shot from a tight angle to the right of Korpisalo snuck in for an unassisted score.

Columbus closed within 2-1 later in the period when Foligno redirected a shot by defenseman David Savard from in front of the goal past Lundqvist.

However, the Rangers responded quickly with a goal from Zuccarello, his career-high 26th of the season, at 18:14 for a 3-1 lead heading into the second intermission. Zuccarello had his initial shot bounce back to him off Blue Jackets defenseman Ryan Murray, and he sent the rebound past Korpisalo.

"I thought we'd get it tied up with the power play and see what happens and kind of give them some payback from the start of the year," Foligno said, "But we couldn't get it done, and we'll just have to wait until next year to get some retribution.

Rangers coach Alain Vigneault liked his team's aggressive start and how it managed to withstand the Blue Jackets' rush at the end to secure his third trip to the playoffs in three seasons at the helm. New York has four games remaining before the playoffs begin next week.

"It's tough to get in the dance," he said. "People don't realize how hard it is to get a chance to play for the Stanley Cup. We finally got our checkmark.

"This group has played good hockey for the most part. Now we can still work for home ice (in the playoffs), and that's what we're going to do."

The only bad news for the Rangers was an upper-body injury that captain Ryan McDonagh sustained in the first period when he blocked a shot on a Blue Jackets power play with his right arm. He finished the period but didn't return to the game.

Vigneault said the injury will be evaluated overnight and there is a good chance a player will be called up from the minor leagues to take McDonagh's place.

The Rangers swept the four-game season series between the Metropolitan Division opponents. New York is third in the division with 97 points, three behind the second-place Pittsburgh Penguins, with three games remaining before the playoffs begin next week.

Korpisalo finished with 26 saves for Columbus, which has three games left in a disappointing season.

"We just weren't sharp moving the puck," said Blue Jackets coach John Tortorella, a former Rangers coach. "They were just quicker. ... We had an opportunity at the end to maybe tie it up, but it just didn't happen."

NOTES: The Rangers entered the final week of the regular season with a three-game losing streak, including two losses to non-playoff qualifiers. They were outscored 5-2 in the first period of their previous four games. ... Rookie G Joonas Korpisalo made his second consecutive start for the Blue Jackets ahead of regular G Sergei Bobrovsky. Korpisalo had 26 saves in Columbus' 5-1 win over Carolina on Saturday. ... F Jared Boll was on the Blue Jackets' fourth line instead of F Scott Hartnell, who hasn't scored since March 4. ... The Rangers finish the regular season with three home games, starting Tuesday night against Tampa Bay. The Blue Jackets play two of their last three on the road, including Wednesday at Toronto. ... Blue Jackets D Cody Goloubef sustained an oblique injury in the opening period and didn't return.