A commanding second-half performance by Forest started their New Year in the pouring rain in emphatic fashion.
The vital points were enough to cut the deficit toward safety to three points off Cardiff City before their showdown on Monday.
Stoke City looked the more lively side in the opening minutes with former Leicester striker Ade Akinbiyi a thorn in the side of the Forest defence.
He nearly put his side in front in the first minute when Paul Gerrard tipped over the bar and the same player was unable to score from close range, scuffing his header inches wide of goal.
Forest had their best spell of the game midway through the second half when Potters' goalkeeper Steve Simonsen came under siege parrying long range efforts from John Thompson, Bopp and Shaun Derry.
Despite his heroics the away keeper was left helpless on 68 minutes when Bopp finally put his side in front.
Irish international Andy Reid stormed down the left wing to curl an inch-perfect cross for the young German to slot the ball past Simonsen much to the delight of the home faithful.
Stoke's chances of stealing anything suffered a knockout blow five minutes before the end when Clint Hill was shown a deserved red card for a retaliation on Thompson.
Ten-man Stoke surged forward in an effort to level things but the Forest defence held firm to secure a vital success in their battle to beat the drop.
The away side were even more depleted before the final whistle when their captain Clive Clarke was sent off following a dispute with the match officials.