A first half strike from Gary Holt and a 57th-minute header from James Perch put Forest firmly in the driving seat, before an injury time penalty from substitute Nathan Tyson sealed a 3-0 success.
This was a one-sided encounter in which Cheltenham keeper Shane Higgs performed heroically, with Forest seeing a host of chances go begging before their Jack Lester inspired opening strike in the 32nd minute.
But, even despite their win, the afternoon was to end on a sour note as Bristol City netted a late winner at Doncaster to maintain their four-point advantage over Forest, prior to the two sides' meeting at Ashton Gate next Saturday.
Forest had begun in bright fashion as a Kris Commons pass sent Lester racing clear, only for Armstrong to make up ground on the Forest striker and tackle before he could get a shot away.
Forest continued to pressure and should have scored as they carved out two fine opportunities in the ninth minute. The first came as Lester robbed Shane Duff of possession in his own box and cut back for Commons to drive a shot against the foot of the post and, as the Cheltenham defence regained their composure, Lester set-up another chance with a neat headed knock down for Lewis McGugan, who hammered badly over from five yards.
McGugan came close with a powerful, curling free-kick that took a deflection that guided it narrowly over the bar for a corner - from which Ian Breckin had a towering header cleared off the line.
It was no surprise when Forest did make the breakthrough, as Lester rampaged through the Cheltenham defence, before feeding Gary Holt, who fired the ball into the bottom corner of the net.
Cheltenham's only effort of the first period was a Denes Rosa shot that dipped just over.
Normal service was resumed after the interval as Commons crossed for Grant Holt to work Higgs with another header - before Forest added an inevitable second. Grant Holt found space on the left to cross to the far post for Perch to head home in the 57th minute.
Perch almost struck again with a shot that was deflected wide of the post, while Grant Holt was himself again narrowly off target.
Melligan drove a vicious volley wide of the post as Cheltenham finally forced some pressure, but it was Forest who struck again as a Duff challenge on Luke Chambers saw Forest awarded an injury time penalty, which was confidently converted by substitute Tyson.