San Jose (2-2-1) got goals from Marcus Sorensen and Joonas Donskoi, and Aaron Dell, who started for the second straight game, made 24 saves. Brent Burns had two assists.
The Sharks outshot the Rangers 43-27, including 33-15 in the first two periods. They have outshot their five opponents 192-126 this season.
"You have to tip your hat to Lundqvist, he's a great goalie and that was a great effort by him keeping them in it through 40 minutes," Sharks coach Peter DeBoer said. "You knew they were going to push at some point. They're a good team and they're trying for their first win. They pushed in the third, but the shots were 11-10 [in favor of the Rangers], so it wasn't like we sat back. Just one of those games, not much you can do."
Sorensen gave San Jose a 1-0 lead with the first shorthanded goal of his NHL career at 4:31 of the first period. Sorensen, playing in his 56th NHL game, made an inside-outside move on Skjei and scored with a shot into the top-right corner from the left circle.