The 18-year-old fired home the only goal of the game with a 20-yard stunner five minutes from time to settle the nerves at the City Ground.
Forest had looked like dropping two valuable points in their bid to catch second-placed Bristol City as Ronnie Jepson's side frustrated them in a tense match.
Goalkeeper Romain Larrieu had been the hero for much of the game with a number of stunning saves to keep Colin Calderwood's promotion-chasing outfit at bay until McGugan stepped up to save the day.
His goal means Forest kept up the pressure in the race to earn automatic promotion.
Starting the day four points adrift of Gary Johnson's Bristol City side, Forest knew they couldn't afford any more slip ups before facing them on the road at the end of the month.
But Jepson's side hadn't read the script with Larrieu keeping the scores level with a number of impressive stops to deny Junior Agogo and Jack Lester in particular.
The visitors had also rode their luck with Kris Commons guilty of missing a golden opportunity.
The match looked like ending in a stalemate with Luke Chambers denied twice in the second half before McGugan stepped up with his decisive strike late on.
It might have been more with substitute Nathan Tyson fluffing two more chances as Gillingham sought an equaliser, but Forest had done enough to secure three crucial points.