A Lewis Grabban strike saw Forest respond within five minutes of going behind to Maxime Biamou's opener in the first half before Michael Rose's own goal just after half-time proved decisive to seal the victory for The Reds.
Forest had to defend resolutely to keep the Sky Blues at bay and they did just that to secure a vital three points on the road.
Chris Hughton made just one change to the side that drew with Barnsley on Saturday as the injured Samba Sow was replaced in the starting line-up by James Garner while there was a place on the bench for his fellow deadline-day signing Glenn Murray as Alex Mighten missed out on the squad altogether.
There was a bright start to the game as Cyrus Christie's low cross in just the second minute almost found the arriving Lewis Grabban at the back post, before Coventry applied some pressure on Brice Samba's goal with Dominic Hyam almost forcing the ball over the line but committed a foul, then Samba was equal to Gustavo Hamer's effort from the edge of the box.
The wet conditions made it difficult for both sides, with the ball skipping off the surface, but Forest were battling hard and looking for the opening goal. Grabban got down the right once more on 13 with his cross too high for the arriving Sammy Ameobi at the back post, but on 17 minutes The Reds found themselves behind.
Filip Krovinovic was on the receiving end of a strong challenge on halfway, with no foul given, and Coventry broke forward with the ball arriving with Maxime Biamou on the right corner of the penalty area. He cut inside and hit a rifled effort across goal and into the far corner past the outstretched Samba.
The Reds weren't behind for long though as on 22 minutes they were level through Grabban. A long ball out to the left found Ameobi who beat his man and pulled the ball back from the byline to the penalty spot where the Forest captain arrived to slot into the bottom corner of the net.
An entertaining opening half continued and three successive corners just shy of the half-hour mark led to three opportunities for The Reds. The first delivery from Krovinovic was flashed wide of his own goal by Victor Gyokeres, the second delivery from the on-loan Benfica man was headed narrowly over his own bar by another Coventry defender and then Grabban flicked the third delivery, this time from Anthony Knockaert, towards the far post but it landed on the roof of the net.
Knockaert fired into the side netting towards the end of the first period, but the teams went in level at the break with Forest the side on top.
They didn't have to wait long to get the goal that their attacking play deserved as the took the lead on 53 minutes. Some neat play between Garner and Knockaert set Cyrus Christie on the overlap down the right. He played a superb cross into the box which arrived at an awkward height for substitute Michael Rose who could only divert the ball into his own net from inside the six-yard box.
Coventry showed a good response to going behind, applying some pressure on Samba's goal but the Forest rearguard stood firm. City came close to equalising on the hour-mark though as Leo Ostigard met a corner at the back post, fired a terrific header towards the far corner but Grabban was on hand to head the ball clear off the line.
The home side continued to press for the leveller, with Matty James shooting straight at Samba and Biamou firing wide at the near post, but The Reds were keeping them at bay as they held on to their advantage. Into the final 15 minutes and Hamer volleyed over the bar from the edge of the box and half-time substitute Dacosta continued to be a threat as his teasing delivery from the right was well gathered by Samba.
Another Coventry sub, Amadou Bakayoko, suffered a nasty looking head injury in the final minute of five added on at the end of the 90, meaning that the game went into 13 aditional minutes, but Forest held out for a vital three points at St Andrew's.
Forest: Samba; Christie, Figueiredo, Worrall, Bong; Garner, Cafu (Colback 71'); Ameobi (Freeman 46'), Krovinovic (Blackett 84'), Knockaert; Grabban (c) (Murray 76')
Unused subs: Smith, Mbe Soh, Jenkinson, Lolley, Taylor
Goals: Grabban 22', Rose own goal 53'
Bookings: Knockaert 54', Krovinovic 74', Figueiredo 90', Colback 90', Bong 90'
Coventry: Marosi; Pask (Dacosta 46'), Ostigard, Hyam (c), McCallum; Sheaf (Rose 46'), James, Hamer; O'Hare, Biamou, Gyokeres (Bakayoko 71', Jobello 90')
Unused subs: Billson, Allen, Shipley, Eccles, Bapaga
Goal: Biamou 17'
Booking: O'Hare 53'
Referee: Tony Harrington
