The Sky Blues claimed all three points thanks to a Gary McSheffrey penalty and a fine individual goal from Dele Adebola against a very poor Forest side.
However, Coventry's night was marred just before the end of the game when Stephen Hughes was stretchered off after going down injured in his own box.
Gary Megson opted to play three centre-backs as Forest looked to end a run of three straight draws that followed the 6-0 thrashing at Ipswich.
Micky Adams made just one change to the side that beat Brighton on Saturday as Adebola was handed a starting berth with Claus Jorgensen dropping out of the 16 due to injury.
Coventry were on top in terms of possession early on but the best opening chances fell to the visitors.
Gareth Taylor scuffed a shot wide of the post when he had time to steady himself in the fourth minute before James Perch saw an effort deflected over the bar from the edge of the area.
Coventry got in a mess from the resulting Kris Commons corner as Michael Doyle sliced the ball at the near post before Adebola headed out of keeper Luke Steele's hands. The home side eventually cleared.
Adebola was in the thick of it at the other end and was holding up the ball superbly to allow City's midfield to join in the attack.
The big striker came close to scoring in the 12th minute when he got on the end of Lloyd Dyer's cross but his header was just wide.
The Sky Blues took the lead in the 23rd minute from the penalty spot. Steve Staunton planted a perfect free-kick onto the head of Hughes who put the ball back across goal.
There didn't seem to be much danger but it bounced up and caught Taylor on the arm and referee Andy D'Urso had no hesitation in pointing to the penalty spot.
McSheffrey stepped up and blasted his post-kick past Paul Gerrard, whose mind-games failed to have any bearing on the little striker.
Forest's formation wasn't working as it was Coventry who looked like they had the extra man in midfield while Shaun Goater and Adebola were getting the better of the three centre-backs.
It could have been two just after the half-hour mark when McSheffrey shot from the edge of the box and Gerrard spilled the ball. Adebola was following in but the keeper redeemed himself with an excellent point-blank stop.
McSheffrey shot over from distance before Adebola doubled Coventry's lead four minutes before the break.
The former Birmingham City targetman picked up a pass from Hughes and drove between two defenders before poking his shot under the body of Gerrard for a terrific individual goal.
It was all Coventry at the start of the second period as Forest struggled to cope with the home side's attack.
Hughes was played in by Staunton in the 49th minute but for once the Sky Blues captain chose the wrong option and shot from a tight angle allowing Gerrard to save comfortably.
Taylor had a free header at the other end from Commons' cross but the striker failed to connect.
McSheffrey tested Gerrard from distance in the 54th minute and then again from close range a couple of moments later but both times the keeper was equal to the efforts.
Doyle and Hughes were winning the midfield battle and the former shot over the bar on the hour mark after the latter had won the ball in the centre of the field.
McSheffrey had a 62nd shot deflected wide and Richard Duffy blasted over two minutes later.
McSheffrey could have wrapped up the points in the 71st minute when he was clean through on goal but Gerrard stood up to the test and saved well.
Forest had their first shot on goal with 15 minutes to go when Commons tried his luck from long range but Steele was equal to it.
Deep into stoppage time, Taylor headed Commons' cross towards goal but Steele did superbly to turn the ball onto the bar.