Haula got the Hurricanes within two at 15:41 of the third period to make it 4-2, but Tomas Hertl scored an empty-net goal at 19:07 for the 5-2 final. Kane had an assist on Hertl's goal.
The Sharks won the special teams battle, going 2-for-4 on the power play while killing off all four Hurricanes power plays.
"We're moving our feet, we're pressuring the opposition trying to force them to make plays a little quicker than they'd like to," Goodrow said.
Brind'Amour said he was not pleased with Carolina's special-teams play.
"We had no attention to detail," he said. "There are going to be lots of penalties, it's just that way now. You have to do a better job at killing them off."