TORONTO -- The New York Rangers had their chances, a lot of them. They were continually thwarted, however, by Toronto Maple Leafs goaltender Frederik Andersen.

They remained patient when frustration might have been expected and it paid off with a 2-1 shootout victory.

They needed a third-period tying goal by J.T. Miller after the Maple Leafs were clinging to the lead provided by a goal by Connor Brown in the first period that otherwise was dominated by the Rangers.

Rangers goaltender Henrik Lundqvist also was solid, stopping two breakaways in the final minute of overtime to make the shootout possible.

The Maple Leafs (28-20-12) were hoping to avoid the shootout.

"That was the plan but they wouldn't let us have the puck," Maple Leafs coach Mike Babcock said. "We hit the bar in overtime and it's not like we're not trying to win, we're trying to win the shootout too and today would have been a good one to win for (Andersen). Freddy had done everything for us, it would have been nice if we scored some goals for him."

Andersen made 37 saves.

Lundqvist, who made 32 saves in the game, took a simple approach to the breakaways. "Stop it," he said. "Seriously, I try to keep my focus real simple right now and it's been paying off the last few weeks. ... That's what I did well on the breakaways, just be patient."

The Rangers (39-19-2) got two shootout goals in two chances with Mika Zibanejad getting what proved to be the decisive one as the Maple Leafs scored only once in three attempts.

"We were definitely playing the right away," Rangers coach Alain Vigneault said. "I thought we had a great first period, quite a few Grade A opportunities. Their goaltender made some big saves. We had one missed assignment in the first period and the puck ended up in the back of our net. But I really like how we were playing and that's what we said going into the third, just continue doing what we've been doing."

The Rangers also had their chances in overtime. Miller was sent in alone early in the five-minute period but fanned on his shot and Andersen followed with a couple good saves.

Brown scored his 15th goal of the season on a rebound at 10:56 of the first period.

Andersen was the difference for Toronto in the period, making several good saves. One in particular came against New York right winger Michael Grabner, who was alone in front of the goal with Andersen to one side of the net. Andersen was able to make the stop. "I saw he tried to pass it back and I don't think he put it where he wanted to," Andersen said. "I didn't get very far over but he put it right on my pad."

The Rangers had a 25-18 edge in shots on goal after two periods.

"The chances we created, we had a feeling we were going to score at some point, if we didn't fall out of our system," Zibanejad said. "

"The key there was not to try to do too much as a goalie," Lundqvist said. "We had enough chances to score and win the game. So, to me, it was about keeping the score at 1-0 just to give us a chance and hope sooner or late it's going to pay off, all the chances."

The Rangers went on a power play at 8:48 of the third period when Toronto defenseman Nikita Zaitsev took a tripping penalty.

The penalty had just expired when Miller knocked in a rebound for his 19th goal of the season at 10:50.

"I thought before that in the third period we were holding on to the lead well," Brown said. "We were playing in their end. There are some things we can do better but it wasn't a terrible effort and real good one by Andersen."

Said Vigneault: "For us right now, it's playing the right way. Tonight, we did that. We moved the puck, I thought really well, got some great looks, and were able to get it done."

NOTES: Rangers D Kevin Klein (upper-body injury) was a late scratch. ... Toronto C Mitch Marner (right shoulder) missed his fourth straight game Thursday and is on injured reserve. A return date has not been set. ...Toronto D Connor Carrick (upper body), who was injured in the first period Tuesday in the victory over the Winnipeg Jets, did not play Thursday. He is listed as day-to-day. D Alexey Marchenko took Carrick's place Thursday in his first game with the Maple Leafs since being claimed off waivers from the Detroit Red Wings on Feb. 4. ... Rangers RW Brandon Pirri was back in the lineup Thursday, replacing RW Pavel Buchnevich. ... The Rangers play their next game Saturday when they visit the New Jersey Devils. ... The Maple Leafs are home to the Montreal Canadiens on Saturday.