Earnshaw and an own goal from Bondz N'Gala ensured the Reds will have home advantage in the second leg of their play-off semi-final at the City Ground, where they have lost just three league games this season.
And Billy Davies' men will be hoping that the next time they return to the City Ground it will be to secure a trip to Wembley as they bid to win promotion to the Premier League.
Forest enjoyed the better of the early exchanges but were unable to find a way past David Stockdale in the Plymouth goal.
Nathan Tyson wasted the chance to break the deadlock after just five minutes but, after Stockdale came out to narrow the angle, the striker sent his effort over the bar.
Stockdale was called into action again soon after as Earnshaw tried to beat him with a first-time chip, but the 24-year-old clawed the Welshman's strike round a post to keep the score goalless.
However, Earnshaw made no mistake next time around as he netted the opening goal of the game after 19 minutes. Radoslaw Majewski's pass into the centre of the area split the Plymouth defence apart and Earnshaw was on hand to fire a shot beyond Stockdale.
Forest could have doubled their advantage five minutes later, but Tyson's effort was well parried by Stockdale.
At the other end, goalkeeper Lee Camp, who was recently named as the club's official Player of the Year, dived to his left to deny Alan Judge before Guy Moussi cleared the danger.
Moussi then made a crucial contribution in attack as the Reds increased their lead after 34 minutes. The midfielder's driven cross came off a combination of bodies including Dexter Blackstock, but the goal was eventually credited as a N'Gala own goal.
The hosts pushed for a third in the final minutes of the first half, but James Perch's strike was deflected wide for a corner by Judge before Blackstock's volley flew over the bar.
Plymouth's misery continued when Reda Johnson was forced off injured in stoppage time.
Nottingham Forest looked dangerous in attack and almost added a third within seven minutes of the restart when Chris Cohen, who was making his 200th career league start set up Blackstock, but the striker's header sailed over.
Plymouth, whose relegation was confirmed after Monday's defeat by Newcastle, tried to find a way back into the game but Bradley Wright-Phillips saw his effort blocked by Forest defender Wes Morgan before Kari Arnason sent a header over the top.
Tyson was forced out of the action with what appeared to be cramp six minutes from time, while the visitors lost Kari Arnason, before Forest put the icing on the cake with a third in injury time.
Paul Anderson scored from Lewis McGugan's touch as the two substitutes combined to secure the Reds' first double over their Pilgrims since the 1955/56 season.