NEW YORK, N.Y. - The New York Rangers needed more than a season-high 49 shots to beat Ryan Miller and Vancouver. They needed just as much patience.

J.T. Miller scooped up his own rebound and scored on a wraparound 3:54 into overtime, and the Rangers rallied for a 3-2 victory over the Canucks on Tuesday night.

"I think anyone is naturally a little bit frustrated," said New York captain Ryan McDonagh, who had the primary assist on the game-winner. "We were getting some high-quality looks there, putting a lot of pucks to them, but that's a goalie that's been well-tested and he can steal games for them. I'm glad that we continued to press and found a way to get a couple more."

The Rangers could easily have given in to the frustration. They not only outshot Vancouver 49-20, they rang four other shots off the post.

While goalie Henrik Lundqvist could feel the frustration creeping in, he said the Rangers have shown the ability to rally in recent weeks.

"We believe that we can turn games around," Lundqvist said.

They did in the third period when Mats Zuccarello tied it with a goal in close with 8:14 left.

J.T. Miller came through for New York in overtime with his 10th of the season.

It was a play that developed because Derek Stepan, who scored the Rangers' first goal, had been on the ice for an extended shift. He looked over to the bench for help, and J.T. Miller jumped on the ice after the centre got to the boards.

McDonagh fed him the puck in the left circle and J.T. Miller fired at Ryan Miller, who made the save. The Rangers' forward collected his own rebound, skated around the net and wrapped the puck inside the post before the Canucks ' goalie could close off the corner.

"If I remember correctly, he didn't see the puck fall and it gave me just enough time to go around the net," J.T. Miller said.

Ryan Miller made 46 saves in defeat, one fewer than he had in a win over the New York Islanders on Sunday.

"They're opportunistic, and they are also able to get in the zone and work around," Ryan Miller said of the Rangers. "They're a strong team."

Andrew Burrows and Sven Baertschi scored for the Canucks, who played without captain Henrik Sedin. He is sidelined with an upper-body injury.

The Rangers outshot the Canucks 19-3 in the third period and overtime.

The Canucks, who are 8-3-3 in their last 14 games, led 2-1 after two periods despite being outshot 30-17.

Baertschi gave Vancouver the lead at 9:02 of the first period with his eighth goal. Bo Horvat did all the work, skating around Rangers defenceman Dan Boyle, going behind the net and centring a pass that Baertschi ripped past a defenceless Lundqvist.

Stepan tied the game early in the second period with the officials about to call a delayed penalty on Vancouver. New York got the extra skater on and Stepan eventually slammed home a rebound of Chris Kreider's shot that Rick Nash had nudged in the crease.

Emerson Etem, acquired by the Rangers in the off-season and then shipped to the Canucks earlier this month after doing little in his short stint, got some payback in the second period. Linden Vey won a puck in the corner and sent to it Etem in the right circle. He fired it across the crease for a tap-in by Burrows, who had not scored since Nov. 21.

NOTES: Rangers C Derick Brassard, who has 15 goals, missed his first game of the season with the flu. Kevin Hayes replaced him on a line with Nash and Zuccarello. ... Jared McCann replaced Henrik Sedin on a line with Daniel Sedin and Jannik Hansen. ... New York D Kevin Klein returned to the lineup after sitting out a game with an injured thumb. ... Eagles co-founder, singer and songwriter Glenn Frey, who died Monday, was honoured in a musical tribute between the first and second periods. ... Linesman Steve Miller was hit in the helmet on a clearing pass in the third period and was down for a couple of minutes. He stayed in the game. ... This was the fourth game of a six-game road trip for Vancouver.