The win, New York's fourth in five games, moved the Rangers into a tie with Carolina for eighth in the Eastern Conference - the cutoff for the playoffs.
Matt Cullen also scored in the shootout against Hurricanes backup John Grahame, and Henrik Lundqvist turned aside Justin Williams and Ray Whitney in the tiebreaker. Williams got the Hurricanes even at 1 with a second-period goal.
Jagr has shootout goals in two of his last three tries after an 0-for-4 start this season. Lundqvist made 30 saves overall.
The Rangers earned a point for the seventh straight game (5-0-2) and played overtime for the sixth time in nine contests. Carolina pressed for the winner after Michael Nylander was called for high-sticking with 1:35 left in overtime, but Lundqvist held his ground.
Malik, routinely booed at Madison Square Garden, briefly won the home rooters over when he scored his first goal since Feb. 6, 2006. He took a pass from Jagr and raced up ice. Malik, who has 30 NHL goals in 594 games, fired a shot from the high slot that was blocked by goalie Cam Ward.
Malik got to the rebound, kicked the puck to his stick, and backhanded a shot past Ward's pad and inside the right post to make it 1-0 at 9:13 of the first period.
Jagr, questionable after sitting out the third period and overtime of New York's 3-2 loss at Pittsburgh on Saturday, has 11 assists in 16 games.
The Hurricanes tied it on Williams' career-high 33rd goal of the season. Rod Brind'Amour found him in the slot for a shot that sneaked under Lundqvist's right pad 10:04 into the second.
Grahame had a bit of an adventure shortly after Ward was forced from the game due to a cut on his left leg with 8:37 left in the second.
Grahame skated to his right to play the puck, negating an icing call. He swept the puck to the boards, but Jed Ortmeyer was there and sent a shot back toward the vacated net. Grahame dived across with his stick extended as the puck hit the right post and then caromed off the crossbar.
A video review determined that the puck never crossed the line.
Grahame was sharper in the third period when the Rangers had three power-play chances and heard pleas from the crowd to, "Shoot the Puck!"
New York went 0-for-5 with the advantage Saturday against Pittsburgh, including one power play when they made 25 passes without putting the puck on net. The Rangers were 0-for-5 again with only seven shots.
Grahame deflected a hard drive by Paul Mara out of play, then turned aside Nylander and Brad Isbister in front later in the period. He finished with 13 saves but stopped only Nylander in the shootout.
Lundqvist, who owns the NHL's lowest goals-against average since the all-star break, also looked good. He did the splits to deny Cory Stillman in front during the third.
Notes: Jagr, who has 896 NHL assists, is five behind former Rangers coach Bryan Trottier on the career list. ... Williams topped last season's goal total Friday when he scored No. 32 against Washington. ... Ward appeared to be cut by the skate of Isbister. The MVP of last year's playoffs stopped 12 of 13 shots.