Rask scored from in close on the rebound of a Skinner shot with 2:40 left to make it 3-2.
"That's where you've got to go to score," Peters said. "The guys that aren't getting inside the hash marks, in tight to the net, they're not getting anything done offensively."
The Hurricanes took a 1-0 lead when Williams scored on the first shot of the game at 1:37 of the first period.
Ducks center Ryan Getzlaf, who returned to the lineup after missing the previous 19 games following surgery for a facial fracture, lost a faceoff in the Anaheim zone on his first shift, leading to Williams' goal.
Getzlaf was minus-1 in 19:55. He did not have a shot on goal.
The Ducks tied it 1-1 at 5:55 of the first. Grant emerged with the puck following a battle near the Hurricanes blue line and backhanded it to Shaw on his left. Darling got a piece of Shaw's shot, but the puck was sliding toward the goal line when Grant dove and pushed it across.
It was the third multipoint game of Shaw's NHL career.