Jack Hughes had a goal and an assist, Jesper Bratt scored for the first time in 10 games, and Markstrom made 29 saves for the Devils (25-15-4).
New Jersey ended a stretch of six consecutive road games, the most in a row they'll play away from home this season, with a 1-4-1 record. That includes four straight games on the West Coast before coming back to play the Rangers.
"With that in mind I think it's a good point for us," Devils coach Sheldon Keefe said. "There's things we'd like to do better, plays we'd like to have back, but by in large we did some good things in the game. Obviously, special teams are a major factor in the game. They make a big difference. You can include overtime in that. But all things considered it's a good point for our team. We'd like to have two, but we'll take an important day off (Friday). We need some recovery time here."
Adam Fox gave the Rangers a 1-0 lead with a power-play goal at 12:05 of the first period. It came five seconds into the power play.
Vincent Trocheck won the face-off back to Fox, whose shot from inside the blue line deflected off Johnathan Kovacevic's stick, breaking it, and sailed past Markstrom on the blocker side.
"Right away when 'Foxy' walked into the middle and bombed away, that was perfect," Rangers coach Peter Laviolette said. "To me, when you're putting pucks at the net good things can happen."
Hughes made it 1-1 at 4:03 of the second period. Shesterkin's attempt to rim the puck up the boards and out failed when Ondrej Palat intercepted it at the right-wing half wall. He moved it to Brett Pesce at the point for a shot that Hughes deflected in from in front of the net.
Bratt gave New Jersey a 2-1 lead at 8:28, scoring off the rush with a shortside shot from the left face-off circle.
The play started in the neutral zone, where Dougie Hamilton knocked the puck away from Will Cuylle with a big open-ice hit. Hughes got it at the Devils' blue line and moved it up and across to Bratt, who had speed entering the zone.
Panarin made it 2-2 with a power-play goal at 17:13 of the second, scoring from low in the left circle off a rebound of Zibanejad's shot from high between the circles.
"We did (have momentum), but they're a good team, though, and they've had a good power play for years," Hughes said. "We took a penalty and gave one up on the PK."
The Rangers outshot the Devils 12-6 in the third period, but still needed Shesterkin to stop Dawson Mercer on a shorthanded breakaway at 10:49 to keep it 2-2.
Markstrom robbed Panarin with a point-blank glove save and stopped Zibanejad on a breakaway in the first two minutes of overtime, but Smith and Carrick connected on the 2-on-1 less than a minute later to give the Rangers the win.
"It was awesome," Laviolette said of Carrick scoring. "He's played some really good hockey for us lately. He's been on the attack offensively. He hits and he does a lot of the dirty work in the defensive zone. When a guy like that scores a goal you're really happy for him. Obviously, a big goal for our team, but a big goal for him as well."
NOTES: Hughes extended his point streak against the Rangers to 12 games (14 goals, eight assists). He has more goals (16) and points (28) against the Rangers than any other opponent. … Fox's goal was his second of the season and first past a goalie. He scored an empty-net goal in a 3-2 win against the Buffalo Sabres on Dec. 11. … Arthur Kaliyev made his Rangers and season debut. New York claimed Kaliyev off waivers from the Los Angeles Kings on Monday. The forward got 8:31 of ice time. … Rangers forward Matt Rempe returned after serving an eight-game suspension for boarding/elbowing Dallas Stars defenseman Miro Heiskanen on Dec. 20. Rempe had four hits in 7:47 of ice time.
