The rookie center had given Carolina a score-tying goal 6:06 into the final frame when he inadvertently directed a pass from Jamie McBain past Martin Broduer and into his own net.
The Hurricanes' Joni Pitkanen was credited with the goal.
But Henrique made up for it later when he collected a loose puck along the boards at mid-rink, skated in behind Hurricanes goalie Cam Ward and stuffed it past him in a wraparound move for the decisive score.
Brandon Sutter netted an unassisted, short-handed goal in the opening period for Carolina and Ward turned aside 33 shots.
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