Griess was especially strong moving post to post to stop the Hurricanes on Sunday.
"It's the way they play, they like the wraparounds," said Greiss, who is 7-3-1 against Carolina. "They like to come from the goal line. You can get awkward angles where it's tough to make a clean save or make the rebound go where you want. So it's not the easiest thing."
Anders Lee had a goal and an assist, and Josh Bailey had two assists for the Islanders (5-4-1), who were coming off a 6-1 win at the Philadelphia Flyers on Saturday.
Mrazek made 18 saves for the Hurricanes (6-4-1), who lost for the first time in three games.
"Right from the start, we were a tad off maybe," Carolina coach Rod Brind'Amour said. "And when we were a tad off and we were good, we couldn't find the net and we had a couple breakdowns. Frustrating is a good word for it."
Lee scored on the power play to give the Islanders a 1-0 lead 3:39 into the game when he redirected a pass from Bailey in the slot.