Gareth Taylor's header deep into injury-time saw Forest taste league victory for the first time in 18 matches and piled further misery on Bradford.
The win - a first for Joe Kinnear since replacing Paul Hart - also sees Forest climb out of the bottom three at the expense of arch rivals Derby.
Bradford looked to have done enough to earn a point from a tense game which boiled over 10 minutes from time, when Marlon King and Jason Gavin were both dismissed.
The Bradford defender reacted angrily to a challenge from King, and both men were given there marching orders following an ugly scuffle.
Loan signing Nick Barmby marked his Forest debut by playing in Andy Reid for the opening goal before Dean Windass' free-kick dragged Bradford level.
But Taylor, who had only been on the field for three minutes after replacing Barmby, was to have the last say with a superb header into the top corner from Reid's cross.
Bradford could have taken three vital points themselves, but Windass was unable to hit the target from close range following a blunder from stand-in keeper Barry Roche in a frantic finale.
Forest, who had been boosted by the return of Matthieu Louis-Jean and Gareth Williams from injury, were almost ahead from their first attack when Danny Sonner headed Reid's cross narrowly over bar.
Kinnear started with Barmby alongside King in attack, and the new partnership combined well to play in Reid for the opener.
The Irish midfielder beat Nico Vaesen comfortably from 12 yards after he was released by a deft through ball from Barmby.
Bradford were without the injured Alun Armstrong but still carried a potent threat from set-pieces, with Windass unfortunate not to score when a powerful header was clawed out by Roche.
However, the young keeper could do nothing to stop Windass dragging the Bantams level with his third goal in as many games after 19 minutes.
The striker swept home a wonderful curling effort from 25 yards after he had been fouled by Michael Dawson.
Ronnie Wallwork, starting in the Bradford midfield after his loan from West Brom was extended this week, went close with a dipping volley shortly before the break.
Kinnear threw on former Bradford midfielder Eoin Jess shortly after the hour, and he was an influential figure as Forest pressed hard for a winning goal.
Defeat leaves Bradford with a mountain to climb if they are to avoid relegation and comes as a hammer blow to the club at the end of a week in which they have entered administration for the second time.
Teams
Nottm Forest: Roche, Louis-Jean, Dawson, Walker, Rogers,
Impey (Thompson 82), Williams, Sonner (Jess 64), Reid,
Barmby (Taylor 88), King.
Subs Not Used: Formann, Chopra.
Sent Off: King (80).
Booked: Dawson, Walker.
Goals: Reid 9, Taylor 90.
Bradford: Vaesen, Francis, Wetherall, Gavin, Heckingbottom,
Farrelly (Summerbee 90), Atherton, Wallwork, Emanuel, Windass,
Cadamarteri.
Subs Not Used: Davies, Muirhead, Evans, Forrest.
Sent Off: Gavin (80).
Booked: Atherton, Wallwork, Windass.
Goals: Windass 19.
Att: 26,021
Ref: T Kettle (Maidenhead).
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