In the second period, the Bruins had long stretches of possession in the offensive zone, but they were outshot by the Hurricanes 10-6.
The Hurricanes cut Boston's lead to 2-1 on a power-play goal by rookie defenseman Noah Hanifin at 3:00 of the third period. Hanifin's slap shot went wide of the left post, but the puck rebounded off the end boards, hit the stick of Boston's Kevan Miller and deflected off Rask's skate into the net.
But Beleskey restored Boston's two-goal lead when he scored his second of the night, a wrist shot from the low slot at 6:24. Linemate Ryan Spooner forced a turnover behind the Carolina goal and slipped a quick pass to Beleskey.
"We talked about a play off the draw," said Beleskey, who scored 22 goals for the Anaheim Ducks last season. "I just called for it. He's a great passer, he's got great vision. He just laid it in there for me."
Rask was at his best in the third period when the Bruins had to kill two penalties. On Carolina's second power play, he stopped Kris Versteeg from in close on consecutive shots, extending his pad to make the first save, then fending off Versteeg's backhand bid on the rebound.