The Hurricanes evened their best-of-seven, opening-round series at 1-1, grabbing home-ice advantage thanks chiefly to tremendous goaltending by Cam Ward.
Ward, who was beaten four times Wednesday in the series opener, made 33 saves Friday and did not allow a goal after Zach Parise scored on the power play midway through the opening period.
Carolina tied the game with just 25 seconds left in the first on a power-play goal by Eric Staal, and Ward then dueled Martin Brodeur to a standoff through the second and third periods.
The deciding goal came on a blast by Gleason from the point. Brodeur, owner of the NHL's all-time wins record, was screened on the play and the puck got past him after hitting the skate of New Jersey's Niclas Havelid.
Brodeur, appearing in his 171st playoff game, made 30 saves.
Carolina will host the third game of the series Sunday.
Notable deaths of 2014 [PHOTOS]