The Rangers moved into a tie with Ottawa and the New York Islanders for the final three playoff spots in the Eastern Conference, two points in front of ninth-place Winnipeg.
Ottawa, the Rangers and the Islanders are all five points behind Toronto for the No. 5 position in the playoff race.
Phil Kessell produced both of Toronto's goals, the second coming midway through the third period that created a 2-2 tie.
New York had taken the lead on goals by Carl Hagelin and Ryan McDonagh during the final 10 minutes of the middle period.
Lundqvist made 23 saves to get the win. James Reimer stopped 26-of-28 shots before letting in Zuccarello's goal in the shootout.
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