A pair of spectacular strikes from Kris Commons and a bundled goal from David Prutton emphasised the home side's domination over a Bournemouth side, which played for more than 45 minutes with ten men after skipper Neil Young was controversially red-carded late in the first half for a professional foul.
But, with Bristol City claiming victory at Carlisle, Colin Calderwood's side still need to close a four-point gap between them and the Robins, in the space of only two matches.
Calderwood will still have been encouraged by his side's performance, which saw Jack Lester, Grant Holt and Felix Bastians all come close to increasing Bournemouth's misery.
But they are likely to have to maintain their form in the end of season showpiece, if they are to have any hope of earning a place in the Championship.
Forest were desperate for the win to maintain their hopes of grabbing a place in the top two and it showed as they began in urgent fashion, with Lester lashing an early chance narrowly over.
David McGoldrick, a former Notts County youth team product, seemed intent on haunting their city rivals, testing Forest keeper Paul Smith on no less than three separate occasions with powerful, driven shots, during a first half in which Bournemouth were a significant threat on the break.
But while the Cherries were also left to rue missed chances from both Steve Fletcher and Sam Vokes, Forest were more ruthless. Grant Holt had forced a strong save from keeper Stewart with a powerful diving header from a Commons cross.
But the keeper could do little when Commons cut in from the flank and struck an unstoppable 25-yard drive into the top-left corner of the net with his supposedly weaker right foot.
Things got worse for the visitors when they were reduced to 10 men, in somewhat harsh fashion, as skipper Young saw red.
The defender had been somewhat reckless in his challenge after giving the ball away to Lester inside his own half - but there seemed to be at least two Bournemouth players still between Lester and the goal.
Nevertheless Bournemouth found themselves a man down - and Forest took full advantage.
Lester shook the post with a thundering shot five minutes into the second half. And in the 54th minute, Forest got their second, as Commons struck with venom for a second time, rifling another long-range effort powerfully into the back of the net, this time off the underside of the bar.
The confidence drained from Bournemouth - but Forest were in no mood for mercy and, following an emphatic spell of pressure, Prutton bundled home the third at the far post, converting a cross from Commons.
It could have been worse for Bournemouth, but with Bristol City claiming a vital win, this may well have felt like a defeat for Forest too.