Gunter, a £1.75million summer signing from Tottenham, played a neat one-two with Dexter Blackstock.
He was fortunate that substitute defender James Chester slipped when he collected the return ball inside the box, but Gunter confidently beat Romain Larrieu with a low shot.
Forest remain unbeaten on their travels since mid-March, although this was only their first away win since the end of February, while bottom-of-the-table Argyle have made their worst start to a season for 28 years.
Home Park was full for the first time in five years as Plymouth launched their bid to be a host city for England's 2018 World Cup bid, and the feel-good factor spread to Paul Sturrock's players as they made a bright start to the game.
After an early scare from a Blackstock header, Argyle should have taken the lead through Jamie Mackie but he poked a driven, low cross wide from eight yards out.
The winger almost made amends midway through the first half following a piece of individual brilliance. Mackie collected possession on the left touchline, he backed three Forest defenders into the box and only a solid foot from keeper Lee Camp denied him a goal.
A dipping shot from Radoslaw Majewski skimmed the top of the net before Argyle lost Icelandic centre-back Kari Arnason to injury after 35 minutes.
He was replaced by Chester, whose first real involvement was his ill-timed slip to allow Gunter a clear shot at goal.
Joe Garner should have extended Forest's lead early in the second half but he sliced his shot wide from 10 yards out.
Majewski tried to catch out Larrieu with a free-kick on the edge of the box just after the hour mark, but the Pole's shot curled just over the crossbar.
Argyle should have been awarded a penalty in the 70th minute when Kelvin Wilson appeared to unfairly halt Chester's path to goal, but referee Andy Woolmer waved away the appeals.
Substitute Alan Judge looked lively when he came on. The midfielder, on loan from Blackburn, dragged a half-volley wide before stinging Camp's palms with a well-struck shot on the run with five minutes remaining, but that was as close as Argyle came to an equaliser.
The win moves Forest up to 17th in the table, while Sturrock's side remain five points from the safety mark.