Skipper James Perch drove home just 45 seconds into the second half to lift the Reds out of the relegation zone and take them a step closer to avoiding the drop into League One.
The Sky Blues could have put themselves in the driving seat in the first half but for an astonishing miss from Freddy Eastwood.
But by the end, Forest were unlucky not to have increased their advantage after dominating a second half that saw Chris Cohen come close to adding a second.
Chances were sparse in a cagey opening to the contest but it was Coventry who missed the best of them as good work from Eastwood saw him square a clever ball towards the near post where Clinton Morrison turned smartly but fired straight at Paul Smith.
Forest were not without menace themselves, however, as defender Luke Chambers rose on the edge of the six-yard box to head a Lewis McGugan corner powerfully against the bar.
A remarkably poor piece of finishing from Eastwood denied Coventry the lead in the 29th minute with the forward side-footing wide from barely two yards after being picked out by Morrison at the far post.
McGugan then launched himself into an impressive run that carried him through three challenges, before finally being denied by a desperate challenge from Elliott Ward as he threatened to burst into the box.
Referee Steve Tanner was having a poor match, making several questionable decisions, but none was more mystifying than his decision not to award a penalty to Coventry after Joe Garner had brought down Aron Gunnarsson inside the area, with the Somerset official instead awarding a free-kick on the edge of the box.
Forest did not feel sorry for themselves for long in the second half after powering their way into the lead after only 45 seconds of the restart.
Dexter Blackstock collected a low, lashed cross from McGugan on the edge of the six-yard box before rolling an intelligent ball into the path of Perch, who lashed a confident left-footed finish low into the bottom corner.
Forest should have had a second when Garath McCleary, a half-time substitute, fired over from good position after a Blackstock effort had been charged down.
Cohen was only denied by a strong save from Keiran Westwood after robbing Danny Fox of possession and surging into the box, while Blackstock came close with a lofted, flicked header that dropped just over.
A clever back-heel from Garner almost carved out a second for Forest with Elliott Ward's driven goal-line clearance bouncing back of Blackstock and narrowly wide of the post.
Despite having to hold on under some pressure in injury time, Forest secured a win that took them out of the bottom three.