Fast gave the Rangers a 1-0 lead at 9:35 of the first when he tapped in a pass from Panarin, who has four goals and eight assists during his point streak.
The Sharks outshot the Rangers 22-3 in the first period.
"You couldn't have a better first period than we had," San Jose coach Bob Boughner said. "I thought that we threw a lot at [Shesterkin], a lot of chances. … The personnel that we have in there, we have to almost play a perfect or near-to-perfect game when you are only scoring one or two a night."
The Rangers outshot the Sharks 30-24 in the second and third.
"Obviously, we weren't happy with it at all," Zibanejad said of New York's start. "It was really disappointing, especially the way we played yesterday. It's not the way we wanted, but I think the way we responded to it, we did enough to win today."