Scotland international Miller headed home Peter Whittingham's cross in the 59th minute to clinch Cardiff's first league win in four and keep them three points adrift of second-placed Middlesbrough.
But Forest's miserable run continues. Steve Cotterill's side have lost six and drawn one of their last seven league games and have gone 630 minutes of league action without scoring.
United States striker Robbie Findley added to Cotterill's woes when he was forced out of the game in the sixth minute due to a nasty-looking shoulder injury.
Cotterill was forced to recall Findley and fellow forward Garath McCleary to his starting line-up due to injuries, together with defender Joel Lynch, while Darcy Blake returned at right-back for Cardiff with Rudy Gestede installed up front.
Forest pair Dexter Blackstock and Paul Anderson were both ruled out through injuries sustained in the Boxing Day defeat to Peterborough and Cotterill was dealt another blow when Findley fell awkwardly following a collision with Cardiff goalkeeper David Marshall.
Marshall appeared to bring the American down as he raced on to a deflected through-ball, but received only a yellow card for his infringement, and the Forest striker was subsequently replaced by Matt Derbyshire.
Cardiff looked a threat on the break, but Forest played the better football and went close to breaking their goal drought in the 23rd minute when midfielder Lewis McGugan's shot from inside the penalty area was blocked by Cardiff defender Mark Hudson.
McCleary made a nuisance of himself in the first period, forcing Marshall to hold two efforts and pulling another shot wide, while Cardiff spurned a gilt-edged chance to take the lead when defender Ben Turner planted a free header wide from Whittingham's free-kick.
Forest goalkeeper Lee Camp ensured a goalless first half when saving well from Scottish forward Miller's 25-yard shot just before the break.
Forest continued to hold their own after the restart, working tirelessly to snuff out the threat of the Welsh side's three-pronged attack, but the visitors continued to threaten.
Miller inexplicably misfired when sent through one-on-one with Camp, but the Scot soon atoned to give Cardiff a 59th-minute lead.
Whittingham crossed from the right and Miller managed to redirect the ball with sufficient power to beat Camp into the top corner.
Forest rallied and McGugan lashed a right-footed volley just wide from 25 yards before midfielder Jonathan Greening was off target with his 20-yard effort.
Cardiff defended with steely determination and repelled another Forest corner from McGugan, while Gestede headed Andrew Taylor's cross wide at the other end.
Striker Patrick Bamford and midfielder Andy Reid were sent on for Forest pair Derbyshire and Greening with 11 minutes left, but Cotterill's last throw of the dice came to nought as the visitors refused to buckle.
Lynch fired a 20-yard shot wide in time added on and Marshall punched clear McGugan's free-kick in the 92nd minute.
Source: DSG