The Sabres suffered their 23rd loss, most in the NHL.
The Rangers finally broke the game open in the third on goals by Brad Richards and Mats Zuccarello.
Lundqvist did not allow a goal until Tyler Ennis produced his fifth of the season with 2:16 remaining in regulation.
Miller made 28 saves in taking the loss.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff