Lewis Grabban hit a spectacular effort to make it 2-0 in the 63rd minute and, six minutes after that, James Garner helped them notch up an emphatic success, as he bent a free-kick inside the far post from the left.
But it was Hughton who was left the happier of the two managers, saying: "This has been our best performance in terms of creating chances, of getting into good positions and creating good chances. So I am really pleased, because it has been a good weekend for us, following the win at Cardiff.
"In terms of our all-round performance, this was one of our better ones.
"This was always going to be a completely different game. But we wanted the same from our team. We were able to show that. We created a lot of chances and we got what we deserved.
"Lewis will have enjoyed his goal – and all three were different goals. But his was a really good striker's goal. He has that ability. It has been a difficult stop-start season for him, with him being out with injury for a period of time. But he was very good today.
"Now we want to finish the season as best as we can. What is not yet fact is that we are safe. Everyone is fighting below us. What is fact is that we are playing well enough that we can look forward to the remaining games and hoping to finish as strongly as we can."
The result left Forest on 48 points and looking unlikely to get sucked into the relegation fray – and left former Reds boss Mark Warburton frustrated. Although he feels the physical demands of a unique season are starting to take a toll on his team.
"We are human. We are playing so much football. Both teams looked tired in the first half and that is because we are playing so much football; we are playing games every few days," said Warburton. "When you are playing four or five games in 14 days, you are setting unprecedented challenges for players.
"We have to recognise that there is a standard that we have to maintain; there is a consistency that we want.
"We cannot be below our best, we cannot be complacent, because teams like this will hurt you. But there are demands on these players that we are asking of them.
"Both teams looked tired in the first half. But we looked slow with the ball, which is not like us.
"To give a goal away like that in the 44th minute was very poor on our part. We gave them something to hold on to. They are a good team, they defend well. They played well."