The defeat saw fifth-placed Villa miss the chance to move third and ended a six-game unbeaten Premier League run.
Forest, meanwhile, climbed up to 12th and maintained their strong home record having now only lost two of their last 20 Premier League games at the City Ground.
Forest are typically fast starters in the Premier League this season and caught Villa cold early on as Aina arrowed a fine opener from Harry Toffolo's pull-back into the bottom corner in the fifth minute.
The full-back's first goal for Forest was the club's fourth goal in the opening five minutes of this campaign, which is more than any other Premier League team.
Villa responded with plenty of possession and eventually had their first shot on target in the 36th minute as Nicolo Zaniolo saw his low effort pushed behind by Vlachodimos.
That proved to be Zaniolo's last real involvement in the game as Emery brought off the Italy international at half-time for Leon Bailey.
But just two minutes into the second half the tactical change suffered a setback as Forest doubled their lead following Martinez's mistake.
The 31-year-old failed to deal with Mangala's 20-yard shot as he got a weak hand to it palming the ball upwards with the spin carrying it over the line.
The City Ground's jubilation was then immediately tempered by a minute's applause for Nottingham Panthers ice hockey player Adam Johnson, who died while playing last Saturday.
Villa did step things up as they searched for a route back into the game but they failed to take their chances as Ollie Watkins miscued his header wide, Moussa Diaby was denied by Vlachadimos and Lucas Digne fired over.