Colin Calderwood's side had gone three matches without a win, but a penalty from Junior Agogo and a spectacular strike from Nathan Tyson put them back on track courtesy of a 2-0 win.
There had been a growing sense of frustration among the home fans at half-time but a handball from Shane Sherriff gave Forest the chance to take the lead from the spot in the 50th minute.
And Tyson's volley - rifled in off the underside of the bar in the 78th minute - secured Forest an important win over one of their promotion rivals.
Former Forest striker Gareth Taylor almost returned to haunt his old side within two minutes of kick-off when only a smart save from Paul Smith denied him as he connected with a deft near-post header.
The home side's first chance came following a fine cross field ball from Agogo, headed down by Luke Chambers, which picked out Lewis McGugan in the box.
But, after riding two challenges, the teenage midfielder couldn't engineer room for a shot and the ball was cleared.
Forest had a reasonable penalty claim rejected by referee Mike Thorpe when Antony Kay seemed guilty of holding back Chris Cohen.
At the other end, it took a fine challenge from Kelvin Wilson to deny Chris Greenacre a shooting chance as the Tranmere striker threatened to pounce on the loose ball when a shot from Steve Jennings had taken a favourable deflection.
Arron Davies almost marked his senior debut with a spectacular goal as he sent a dipping volley goalwards with his left boot but Coyne showed fine reactions to palm over.
After the break, Forest began brightly and were awarded a fairly generous looking penalty as a cross from Julian Bennett bounced up onto defender Sherriff's hand.
But Agogo was in no mood for mercy as he stepped up to fire home from the spot, sending a firm, driven shot low to the keeper's left as Coyne plunged to his right.
Midfielder Kay had a half chance to draw Tranmere level after picking up a loose ball on the edge of the box but drove wildly over the bar.
Taylor was also off target when presented with a shooting chance from ten yards.
Forest almost plundered a second on the break as Tyson completed a swift attacking move with a driven shot that was blocked by Robbie Stockdale.
But a goal was not long in coming as Bennett rampaged down the left again and whipped in another superb cross, this time for Tyson, who hammered a volley in off the underside of the bar.