Charlie Austin put the hosts ahead midway through the second half - the striker's fifth goal of the season - and they were on course for a fourth consecutive league win.
But it all went wrong for them seven minutes later when Green failed to control Nedum Onuoha's back-pass and pulled down Chris O'Grady.
He was duly shown the red card and Henri Lansbury drilled the resulting spot-kick past substitute keeper Alex Smithies.
Worse followed for Chris Ramsey's side when Forest's three debutants combined to put them ahead.
Ryan Mendes collected O'Grady's header and released on-loan Benfica forward Oliveira, whose shot took a slight deflection off Onuoha, wrong-footing Smithies.
Forest were the better side for much of the first half and QPR's new signing Gabriele Angella was forced off just after the half-hour mark.
Angella was replaced by Grant Hall after a bandage had failed to stem the bleeding resulting from an earlier arm in the face from O'Grady.
Striker O'Grady, signed on loan from Brighton, was a constant menace to the QPR defence.
He was involved in Forest's best moment of the opening 45 minutes when he cleverly exchanged passes with right-back Eric Lichaj, whose shot was blocked by Green.
Rangers survived another scare when on-loan Lille winger Mendes fired wide after turning away from James Perch.
Forest continued to threaten after the break and Lansbury's deflected effort flashed wide.
Rangers responded with a decent spell of their own.
Debutant Daniel Tozser crossed from the left and Perch misplaced his header at the far post, before Onuoha volleyed wide from Matt Phillips' corner.
Green's blunder was undoubtedly the game's turning point but came after another goalkeeping error had enabled Rangers to take the lead on 65 minutes.
Austin turned away from David Vaughan and unleashed a left-footed shot from near the edge of the penalty area, which Dorus De Vries allowed to squirm past him and into the net.
Once Green was dismissed, and Lansbury had hauled Forest level, QPR folded.
Uncertainty from Smithies led to Onuoha needing to clear O'Grady's overhead kick off the line.
And Mendes went close before eventually setting up Oliveira, whose goal gave Forest their first away victory since February.
Source : PA
Source: PA