Grosenick, making his NHL debut, made 45 stops to earn his first win. He became the 22nd NHL goalkeeper to earn a shutout in his first start. John Gibson of the Anaheim Ducks was the last to accomplish the feat when he shut out the Vancouver Canucks 3-0 on April 17, 2013.
"I didn't feel like it was too terribly tough of a game," said Grosenick, who was called up from Worcester Sharks of the AHL on Wednesday. "It's going to be really special to go back on it."
It was San Jose's third shutout of the season and the first since winning back-to-back shutouts to start the season.
Tomas Hertl scored for the Sharks for his fourth goal of the season.
His goal at 18:46 of the first period came on a Sharks two-on-one drive to the net. Hertl skittered a shot underneath Carolina defenseman Andrej Sekera and between the pads of goalkeeper Anton Khudobin.
Joe Thornton added an empty-net goal with 7.3 seconds left in the game for the Sharks.
Thornton said he felt good for Grosenick and there was a lot of excitement on the bench in the final minute as Carolina tried in vain to score.
"It doesn't matter how long you've been in the league, you get excited to see young players come in and do well," Thornton said. "You get excited yourself. It was nice to get the win."
San Jose, playing its sixth of a seven-game road trip, evened their record to 3-3 on the trip. The Sharks have played 15 of their first 21 games on the road and will play at Buffalo on Tuesday before returning home.
"We've been on the road for a long, long time but we're weathering the storm and hopefully when it's done we can go home and play well at home," Thornton said.
Carolina lost its third straight game having only scored one goal or fewer in each.
"I don't think we've wasted any goalkeeper performances," said Hurricanes captain Eric Staal. "They're doing what they're supposed to do and making the saves. We've got to contribute with some offense. Tonight it was everything but the goals and that can be frustrating."
It marked Carolina's second shutout loss of the season.
Khudobin, the Carolina backup goalkeeper, finished with 17 saves and still is seeking his first win at home.
The Hurricanes embark on a five-game road trip beginning on Tuesday at Dallas.
NOTES: San Jose finished with a season-low 19 shots, which also matched a season-low for shots allowed by the Hurricanes. ... The Sharks were 0 for 1 on the power play, while Carolina was 0 for 2 with the man advantage. ... Carolina RW Alexander Semin missed his second straight game with an upper body injury. ... San Jose C Tomas Hertl has points (1g, 1a) in two straight games. ... Sharks RW Barclay Goodrow got an assist for his first point of the season.