Victory closed the gap between the two sides to five points, with the Baggies set to face in-form Coventry tomorrow night.
Goals from Wes Morgan and Kelvin Wilson ruined former Reds boss Paul Hart's return to the City Ground and left his Palace side struggling to escape the threat of relegation.
But the visitors were rarely in the game, particularly after having Matt Lawrence sent off for handball in the 50th minute.
It was no surprise when Forest took the lead in first-half stoppage time, after dominating a largely one-sided first half in which they had produced some flowing football.
The manner of the goal was something of a shock however as central defender Morgan smashed a spectacular, unstoppable volley from 25 yards that was still rising as it hit the back of the net.
Prior to that, it had taken smart saves from the Palace keeper to deny Paul Anderson, from a similarly impressive volley from the edge of the box, and Robert Earnshaw, after he bent a curling shot high towards the top corner.
Forest skipper Lee Camp did have to make an adept save to push away a swirling free-kick from Palace's top-scorer Darren Ambrose as it threatened to nestle in the bottom corner.
But otherwise the best moment of the first half for Palace boss Hart was the rousing reception he received from the Forest fans, who still hold him in high regard following his time in charge at the City Ground.
With Forest in command, Earnshaw had also lifted a shot into the side-netting and Dexter Blackstock had seen a penalty appeal turned down after appearing to have been impeded by Lawrence as he attempted a diving header.
Palace's woes increased just five minutes into the second half when they found themselves reduced to ten men after Lawrence had raised a hand high into the air to cut out a looping Cohen ball, floated over his head, that would have sent Earnshaw clear, with referee Andy Hall deciding he had prevented a goalscoring opportunity.
Forest's domination, unsurprisingly, only increased, with Anderson and Moussi seeing shots charged down in the box and Earnshaw firing just wide after turning neatly.
Still Palace almost found a way back as the outstanding Darren Ambrose enticed another outstanding stop from Camp with a powerful, precise free-kick that was arrowing towards the top corner.
But when, with his first touch, substitute Nathan Tyson latched onto a throughball from Anderson, beat the advancing Julian Speroni and slotted home from an almost impossible angle, the visitors' resistance was finally ended.