The Sky Blues have not won at the Ricoh Arena since the start of October but had every reason to believe their luck had changed after taking the lead after 93 seconds.
Michael Mifsud pulled defenders out of position with a good run and laid the ball for Guillaume Beuzelin to cross.
The Frenchman swung a deep ball into the box for defender Elliott Ward to strike home on the volley.
Forest tried to hit back and should have levelled 11 minutes in. Robert Earnshaw was played through but could not beat goalkeeper Keiren Westwood from six yards.
Both sides attacked and the Sky Blues should have made more of two good chances.
Beuzelin should have done better with a free header while Michael Doyle failed to properly connect with Jay Tabb's decent ball eight yards from goal.
For Forest, Paul Anderson had a cross-cum-shot tipped over the bar by Westwood
But the Reds managed to level in the 27th minute when Chris Cohen's cross found Earnshaw in space and the Welshman's diving header was placed past Westwood.
But Coventry were back ahead within two minutes. Beuzelin's corner was flicked on by Freddy Eastwood for stand-in captain Clinton Morrison to knock past Lee Camp for his seventh goal of the season.
Both teams struggled to create chances for the reminder of the half but Forest pulled level again in the 61st minute.
Lewis McGugan's free-kick from 30-yards out was met by striker Joe Garner, who headed an unstoppable effort into the top corner of Westwood's net.
Coventry felt they should have had a penalty minutes later when Michael Doyle tumbled in the box but referee Neil Swarbrick booked the Irishman for diving.
Both teams went in search of the winner and City boss Chris Coleman introduced strikers Robbie Simpson and Leon Best to try and snatch a winner.
And they nearly had the win in the 89th minute when Mifsud hit a goal-bound effort towards the terget only for on-loan goalkeeper Camp to pull off a world-class save.