Shesterkin kept it 1-0 early in the second with a sweeping blocker save coming across the crease on Eric Robinson at 6:36 and a save on Rantanen on a 2-on-0 with Jackson Blake at 7:52.
Andersen kicked his left skate out to prevent Chris Kreider from scoring into what appeared to be an open net at 11:03 and Svechnikov's stick check on Sam Carrick stopped him from potentially scoring off a rebound at 12:55.
"That type of stuff obviously is huge," Andersen said of Svechnikov's defensive play. "Obviously he has a good offensive game, but that stuff is just as important if not more on our team. We appreciate that type of effort."
The Hurricanes went ahead 2-0 lead at 19:29, when Rantanen set up Svechnikov in the slot.
But the play started on the other end, when Vincent Trocheck had a short-handed breakaway but chose to try a between-his-legs backhanded pass to K'Andre Miller instead of taking a shot. The pass was broken up by Shayne Gostisbehere.
"Gostisbehere was chasing me down on my forehand," Trocheck said. "I couldn't get the puck on my forehand. I was too tight to Andersen to get around him. He had a tough angle for me. He was right on top of it. I could have shot it and buried it into his chest or tried to make the play to (Miller). Unlucky that it hit his skate."
Gostisbehere moved the puck to Rantanen, who sent it across to Blake. He gave it back to Rantanen, who found Svechnikov in the slot.
"That's hockey, right," Brind'Amour said. "You come down on one end and you don't execute and oh, there's your game. That's the difference in the game, really, probably that play."