Michael Emons, BBC Sport
It was a welcome return to form for Steve Cooper's side after they had drawn four times and lost twice since winning 1-0 at Chelsea on 2 September.
Cooper's big decision in changing his goalkeeper was also vindicated as 29-year-old Greece international Odysseas Vlachodimos, who signed from Benfica on transfer deadline day in September, did well on his debut to frustrate a Villa side that began the weekend as the joint highest scorers in the Premier League.
Ola Aina put Forest ahead inside the opening five minutes and Vlachodimos' save to deny Ollie Watkins immediately after the restart then proved crucial with Orel Mangala doubling the advantage seconds later.
Cooper would have also been delighted with his side's defensive performance, with Moussa Niakhate and Murillo defending excellently throughout for the home team.
The win sees Forest jump up to 12th in the table and it was a well deserved three points as they gained only their third league win of the season.