Harry Cornick gave the visitors a deserved lead but once Sabri Lamouchi's side kicked into gear they proved too good for the division's bottom side, with Lewis Grabban converting a late penalty to reflect their superiority.
Luton have now lost their last 11 away games in all competitions – conceding at least twice in each of them – and will need to end their nightmare form on the road to stand any chance of preserving their place in the second tier.
The hosts made a lethargic start and were given a warning after three minutes when James Bree's free-kick from the left narrowly evaded Matty Pearson and Dan Potts before drifting just wide of the far post.
Eight minutes later Bree was at it again – this time his set-piece picked out Potts who, after panic in the Forest penalty box, fired narrowly over from six yards.
Michael Dawson headed wide from a Joe Lolley corner but the visitors were in the ascendancy and deservedly went in front after 23 minutes.
Pelly-Ruddock Mpanzu played in Potts down the left and he cut the ball back from the byline to Cornick, who steered a low finish past Brice Samba.
Going behind sparked Forest into life and they almost levelled on the half-hour as Lolley's corner was headed towards his own net by Pearson, only for Simon Sluga to produce a fine reflex save.
Forest levelled after 36 minutes when Yuri Ribeiro sprayed a cross-field ball out to the right flank and Lolley jinked inside before his low shot squeezed under Sluga, who should have done better.
The home side might have gone in front in first-half stoppage time but Sluga atoned for his error by keeping the ball out after Silva's free-kick led to a scramble in the Luton six-yard box.
Lolley gave Forest the lead after 57 minutes when Ben Watson picked him out on the right touchline and, after an excellent first touch, the 27-year-old cut inside and gave Sluga no chance with a powerful strike into the top corner.
Unlike Forest, Luton did not respond well to going behind. Joe Worrall should have made the game safe after 68 minutes when Silva's free-kick found him unmarked but the defender failed to hit the target from six yards.
Moments later substitute Sammy Ameobi cut onto his right foot and fired a low effort narrowly past the post from the edge of the box.
James Collins should have rescued a point for Luton 10 minutes from time after being sent clean through but his low effort was turned behind by Samba.
Forest were awarded a penalty late on when Silva's free-kick struck Sonny Bradley's hand in the wall and Grabban made no mistake from 12 yards.