Jussi Jokinen scored the game-winner past the 2.
"I thought he was ready tonight," Carolina coach Kirk Muller said of Peters. "He works hard every day, and he took it into the game. He kept his composure and made the huge saves at the end. He battled through a really tough game and a team that throws everything at the net, so that's a big win for him and the team."
Thomas Greiss stopped 22-of-25 shots for San Jose.
With the score tied at two, Jokinen put Carolina ahead at the 11:55 mark when he deflected Jamie McBain's shot from the right point.
Peters made 16 saves in the final frame.
"Guys are just playing for each other, having fun and working hard," Muller said. "It's a team effort."
Skinner gave Carolina a 1-0 lead 7:31 into the first period. After the Sharks turned the puck over behind their own net, Skinner fired a tough angle shot on net from the goal line. The puck hit off the skate of Boyle and went into the net.
Just over three minutes later, Faulk scored on the power play. Carolina used some nice passing in the offensive zone and Faulk completed a tic-tac-toe goal at the 10:34 mark.
Peters stopped 19 shots over the first two periods to keep the Hurricanes in front, 2-0.
But San Jose got two quick goals early in the third to tie the game. Boyle's snap shot from slot cut the gap to 2-1 at the 1:26 mark.
Burns tied things up over two minutes later. Moore gathered the puck behind the net and made a backhand pass to Burns, whose shot from the bottom of the left circle beat Peters.
"They were bigger and stronger than we were, quite frankly, and all of a sudden in the third period, we found it," Sharks coach Todd McLellan said. "That desperation has to be there earlier."
The Hurricanes have won four of their last five meetings with the Sharks...San Jose leads the Pacific Division by four points over the Coyotes and Kings, who were both idle on Friday...On Thursday, the Sharks acquired Moore and a seventh-round selection in the 2012 NHL Entry Draft from the Tampa Bay Lightning in exchange for a second-round selection, previously acquired from Minnesota, in 2012...San Jose defenseman Douglas Murray missed Friday's game with a throat injury...Hurricanes forward Jiri Tlusty has points in six straight games after recording an assist on Friday...Carolina was without forward Chad LaRose due to an upper-body injury.