The Bluebirds were unchanged following the midweek victory at Coventry, but Rob Earnshaw failed a late fitness test and was missing from the Forest squad.
The speedy Nathan Tyson gave the City defence some anxious moments in the opening quarter but the Bluebirds were solid.
They took the lead in the 18th minute when a Ross McCormack shot rebounded out wide to Paul Parry, who drilled a superb, low shot across Paul Smith and into the far corner.
Tyson then bore down on goal with Peter Enckelman rooted to his line, but Roger Johnson's tackle cleared the danger.
In the 25th minute, the busy McCormack crossed to Jay Bothroyd, but his first-time shot flashed just wide of the post.
There were shouts for a penalty when Joe Ledley went down after a crunching challenge from Wes Morgan, but referee Grant Hegley waved play-on.
Forest boss Davies made a change at the interval with Joe Garner on to form a two-pronged attack with Tyson.
The change gave City more room in midfield but the defence had to be alert as Forest were quick on the break.
Gabor Gyepes was booked on the hour after scything down Tyson and two minutes later a poor back pass from Kevin McNaughton let Tyson in but he scuffed his shot straight at Enckleman.
Tyson did have the ball in the net in the 81st minute but the overworked referee gave the Bluebirds a free-kick for a foul on Darren Purse, who had replaced the injured Gyepes.
City made the game safe with a superb strike from Bothroyd in the 87th minute.
Closed in by two defenders, he made space before curling his shot beyond Smith and into the far corner for his eighth goal of the season.