Game 2 of the best-of-7 first-round series is Monday night.
Noesen's collect-and-finish score at 3:44 of the period finally pushed Carolina into the lead, then Martin Necas added an empty-net clincher from beyond the blue line with 1:32 to go. Those capped a grinding outing for the Hurricanes, who needed plenty of big stops from Frederik Andersen to hang on at home.
Andersen finished with 34 saves and was under a steady bit of pressure with the Islanders finishing with a nine-shot advantage. His stops included a wild one midway through the third when he fell backward after the puck pinged the post, then batted down Noah Dobson's skating-in finishing attempt while essentially seated in the crease.
Evgeny Kuznetsov also scored for Carolina, converting a power play just 95 seconds into his postseason debut with the franchise.
Rookie Kyle MacLean scored in the first period for the Islanders, while Varlamov finished with 23 saves.
The Islanders are in the playoffs for the fifth time in six years, though it wasn't an easy battle to get back. Their up-and-down season included a January coaching change (firing Lane Lambert and hiring Patrick Roy) and a six-game skid as recently as mid-March.
But New York won eight of its last nine to clinch a playoff spot Monday.
The Hurricanes are in the playoffs for the sixth straight year and entered as the favorite to win the Stanley Cup, according to Bet MGM Sportsbook, bolstered by a largely health roster compared to missing critical pieces in each of the last two seasons and trade-deadline acquisitions in Jake Guentzel and Kuznetsov.
The Islanders played without center Jean-Gabriel Pageau after he was knocked from Wednesday's regular-season finale against Pittsburgh due to a lower-body injury, leading MacLean to elevate to the third line. The Hurricanes were missing forward Jesper Fast, who suffered a neck strain that knocked him out of Carolina's finale against Columbus.
The Associated Press contributed.