First-half goals from Dexter Blackstock and Michail Antonio put the hosts in control at the City Ground, with relegation-threatened Rotherham failing to mount a response after the interval.
Forest sit eight points off sixth spot with eight games to go, while Rotherham are six points and two places above the drop zone.
Fulham are only behind Rotherham by virtue of goal difference, as Kit Symons' men dominated but somehow contrived to lose 3-0 at home to Leeds United.
Sam Byram put Leeds ahead against the run of play in the 40th minute and Sol Bamba's second-half header had the visitors in smash-and-grab territory before Kostas Stafylidis saw red for Fulham.
Mirco Antenucci's 88th-minute tap-in sealed the points for Leeds, who move into the top half, while Fulham will reflect on their failure to score despite having 27 shots.
Elsewhere, League Two leaders Burton Albion overcame a dismissal of their own to record a last-gasp 2-1 win against Southend United.
The hosts fell behind to a goal on the stroke of half-time from Barry Corr - who had earlier missed a penalty - with Robbie Weir subsequently sent off for Burton.
But Matthew Palmer's strike brought the home side level before substitute Abdenasser El Khayati's last-minute goal sent Albion five points clear at the summit, while Southend stay fifth.
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