White was the 11th of 12 shooters in the shootout. He also had a goal and an assist in regulation.
Ilya Kovalchuk scored his 39th goal of the season at 19:39 of the second. He and Anssi Salmela had two assists apiece.
Goaltenders Kari Lehtonen and Johan Hedberg combined to surrender four goals on 27 shots for the Thrashers, who rallied from a three-goal second period deficit and had lost three of their previous four contests.
New York, which had won four of five, got one goal apiece from Chris Drury (19) (power play), Nikolai Zherdev (23), Nik Antropov (26) (power play) and Markus Naslund (23).
Drury also had two assists, while Rangers' netminder Stephen Valiquette yielded four goals on 30 shots.
Despite the loss, the Rangers are one point back of Pittsburgh in the battle for the sixth Eastern Conference playoff berth.