Yann Kermorgant's first-half dismissal tilted the game in the visitors' favour and they took full advantage after the break through the in-form Raddy Majewski and then Henri Lansbury.
The play-off places now life just four points away for a Forest side revitalised by the return of Billy Davies to the club.
Davies said afterwards: "The confidence is growing.
"We have 12 games to go and we will give it our best shot.
"I have said to the players we go to the next match and give it a go again.
"We know where we are and what we have to do. We know what sort of team we have and we know we have to add to this team."