Nelson Oliveira scored the only goal of the game, on the hour mark at Elland Road as the Reds made it 13 games unbeaten in the Championship.
Dougie Freedman's side were content to concede possession to their hosts but were equally as dangerous going forward with Robert Tesche also going close.
Forest are now past the 40 point mark and move into the top ten with their victory.
Reaction to come on Footy Mad.