Liam Delap fired Forest ahead just 45 seconds into the second half with a low 20-yard strike, before Alysson headed home his first goal for Villa to level the scores at 1-1.
Ian Maatsen was then forced off with all of Villa's substitutions already used, leaving the hosts to play the closing stages with 10 men, and Igor Jesus punished them with a stoppage-time winner to give Oliver Glasner his first victory as Forest boss and end an eight-match winless run against Unai Emery.
Emery felt his side's first-half performance had been undone by a dramatic shift after the break.
"It was a difficult match in 90 minutes," Emery said. "The first half, we played really fantastic, like we were planning and building the team. We stopped them, dominated, created chances and had corners offensively. The second half was completely different; I don't know why. They started by scoring quickly and we lost our shape, we lost our position like we were in the first half."
The Aston Villa boss was particularly frustrated by the injury to Maatsen, which he felt should have been reviewed by VAR.
"That tackle was one the VAR should have called the referee to look at. From my point of view, it should be a red card," Emery said, while also praising the impact of debutants Ibrahim Mbaye and Johan Manzambi off the bench.
Glasner made late changes after scans on Friday evening ruled out Nikola Milenkovic and Jair Cunha with hamstring injuries, forcing Ousmane Diomande into his first Nottingham Forest start and Ola Aina into an unfamiliar back three.
"Yesterday we had the circumstances when we got the results of the scans at 9.30 in the evening and all of a sudden both centre-backs couldn't play," Glasner said. "I knocked at Ola's and Ousmane's door and told them they will start in a back three. We had a lot of challenges to overcome, which is why I'm very proud of the performance and of the win."
Glasner praised Delap's opener without surprise, given what he sees in training every day.
"He deserved it, but it didn't surprise me because I see it in every training session. It's such a hard strike," Glasner said. "We struggled in the first 10-15 minutes when we needed a big save from Matz Sels. But after 15 minutes we controlled the game better and better. We conceded but again huge credit to the players and how they coped with the situation. It wasn't taking a point back to Nottingham; the mindset was that we all felt it can't be a draw."