The undrafted rookie, in only his second NHL game, had the first goal and first assist of his career. Tanner Glass and Chris Kunitz also scored, with Sidney Crosby setting up both Kunitz and Megna after Nathan Gerbe had levelled the match for Carolina.
The Chicago Blackhawks moved two points ahead of the Minnesota Wild in second place in the Central Division with a 5-1 road win in the meeting of the two sides.
Brandon Saad and Patrick Kane each had a goal and an assist, Kane setting up the go-ahead strike for Sheldon Brookbank in the second period.
The Dallas Stars continue to prop up the division despite holding off a third-period rally to beat the Buffalo Sabres 4-3.
The Vancouver Canucks moved second in the Pacific Division, two points behind the San Jose Sharks, after beating the Washington Capitals 3-2 for their fourth straight win.
Ryan Kesler and Daniel Sedin struck in the third period as the Canucks came from behind to extend their run.
Tomas Plekanec and Alex Galchenyuk scored and Peter Budaj enjoyed a 27-save shut-out as the Montreal Canadiens beat the New York Rangers 2-0.
Elsewhere in the NHL, the league announced on Monday night that Phoenix Coyotes forward Martin Hanzal has been suspended for two games for charging Edmonton Oilers defenseman Jeff Petry during Saturday's game between the sides.
Hanzal was suspended without pay and a league statement read: "Hanzal is considered a repeat offender under the terms of the Collective Bargaining Agreement and, based on his average annual salary, will forfeit 75,609.76 US dollars."
Hanzal will miss this week's games against the Los Angeles Kings on Tuesday and the Nashville Predators on Thursday.