Earnshaw struck his 13th goal of the season in the 13th minute to earn Billy Davies' side the three points, helping them bounce back from consecutive away defeats.
But it also required several smart saves from Lee Camp to hold Posh at bay, as they looked to maintain their fight against relegation to League One.
Peterborough began with a packed five-man midfield and just a lone striker in the form of Craig Mackail-Smith as they attempted to frustrate the home side.
Forest prodded and probed patiently through Paul Anderson and Raddy Majewski early on, while a flick from Dexter Blackstock almost sent strike partner Earnshaw racing clear.
It was Peterborough who, on the break, managed the first effort on goal as Chris Whelpdale bent a shot just around the foot of the post from 20 yards.
But a flowing attack from Forest helped them stamp their authority on the game, as Earnshaw swept home from close range after Anderson had set him up with a clever knock-down from Chris Gunter's deep cross to the far post in the 13th minute.
It could have been 2-0 as Majewski split the visitors' defence with an angled pass that sent Earnshaw surging into the box, where Joe Lewis made a fine block before Gabriel Zakuani headed the loose ball over his own bar as Blackstock waited to pounce.
James Perch, who had been carrying an ankle injury, had to be replaced in the 21st minute by substitute Luke Chambers, who slotted straight into the left-back position.
Forest keeper Camp had to make a smart save to deny Charlie Lee, after he advanced from his holding role in midfield to bend a dangerous shot towards the bottom corner of the net.
The Reds were furious as a lunging tackle from behind by Kerrea Gilbert on Majewski was allowed to go unpunished, with Sergio Torres immediately sending Tommy Rowe clear on goal only for Camp to again come to the rescue with a superb, sprawling save.
A Blackstock header - saved by Lewis - and a low, fizzing shot from Chris Cohen that flashed wide offered a reminder of Forest's own threat before the break.
After Peterborough made two changes at the interval, introducing Dominic Green and Reuben Reid, they started brightly, with Zakuani forcing another impressive save from Camp with a towering header.
Forest began to take control of the game again, but without carving out clear-cut opportunities, as Peterborough defended solidly.
And it took Camp's reactions to deny United an equaliser as sub Green fired a rising shot that was angling inside his near post.
Lewis was performing equally well at the other end however, stretching full length to palm a Cohen effort against the foot of the post, although referee Keith Hill mystifyingly awarded a goal-kick.
And he had to be at his best again to push a driven shot from substitute Garath McCleary wide.