The Rangers finished on top of the Eastern Division and looked every bit the favorite by rolling to a 4-0 advantage.
Lundqvist finished the regular season with the third-most wins in the NHL (39), the fourth best goals-against average (1.97) and the fifth-best save percentage (.930).
He brought only a 15-20 career playoff record into the game, however, and was under pressure to perform at his regular-season level in order to help the Rangers advance.
Milan Michalek broke up Lundqvist's bid for a shutout with 9:55 to play and Erik Condra also scored for the Senators with 2:19 to go.
New York, seeking its first playoff series victory in four years, will host Game 2 on Saturday.
Craig Anderson gave up all four goals on 31 shots. This is the first post-season meeting between the Rangers and Senators.