Goodrow took a pass at the top of the slot from Vincent Trocheck on the rush and beat Sergei Bobrovsky on a wrist shot.
"I don't really remember exactly how it went in," Goodrow said. "I just remember Trocheck made a great pass to me and [Will Cuylle] was driving to the net, opening up the lane, so it was a great play by those two … It feels good, I think, whenever you can do something to help your team. Obviously, I think we played a pretty good game tonight, and it was nice to get rewarded with the win."
The goal came shortly after Goodrow won a face-off in the defensive zone.
"Everybody knows what he brings to the team," Trocheck said of Goodrow. "Every night, he's going to bring the same game. We use him in all different situations. ... In these playoffs, he's been outstanding for us on both ends of the ice."
The best-of-7 series is tied 1-1. Game 3 will be in Sunrise, Florida, on Sunday (3 p.m. ET; ABC, ESPN+, SN, TVAS, CBC).
Trocheck had a goal and an assist, and Igor Shesterkin made 26 saves for the Rangers, the No. 1 seed from the Metropolitan Division. New York is 3-0 in overtime this postseason.
"In overtime, you're just looking for that one," Rangers defenseman Adam Fox said. "... You know how big of a goal it is to make the series 1-1 rather than 2-0. It's massive and you're excited to see that one go in."