The Reds looked to be down and out after Matteo Alberti struck either side of half-time to cancel out Lewis McGugan's penalty.
But midfielder Cohen headed home Luke Chambers' cross to earn a share of the spoils as a young and inexperienced Forest side hung on at the end.
QPR were twice denied by goalline clearances after just seven minutes when first Samuel Di Carmine thundered a shot but Brendan Moloney cleared off the line, before Alberti struck the rebound but Joe Heath produced a stunning block again on the line to save the Reds.
A clash of heads left striker Nathan Tyson with a nasty gash and he had to go off after 15 minutes to further deplete the Forest side.
Skipper for the day Wes Morgan offered a header wide from a corner before Alberti struck a shot on the turn from inside the box only to be denied by the upright.
But on the stroke of half time Forest won a penalty when McGugan chipped in a superb ball for Chambers and he was pulled back by Alberti.
From the penalty spot McGugan made no mistake, sending his former team-mate Lee Camp the wrong way to put Forest ahead.
But three minutes into first-half injury time, Alberti made up for his error when Matt Connolly pulled the ball back from the right byline and the Italian fired beyond Paul Smith to haul his side level.
Alberti struck again two minutes after the break, latching onto Wayne Routledge's flick on, holding off Moloney and firing a shot across goal and into the top corner.
Routledge should have made it three when he flicked the ball over the head of Heath down the right of the box but pulled his shot wide of the far post.
But Forest equalised on 66 minutes out of nothing when Chambers fired in a hopeful deep cross from the right to the back post and Cohen rose superbly to head back into the far corner.
Mikele Leigertwood thought he had put QPR ahead again when meeting a corner from the right only to be denied by a stunning save from Smith.
And Forest dug deep, failing to give in to QPR's late pressure, and they saw out five minutes of injury time to draw 2-2.