Brighton are now seven points adrift of safety with just seven games to go and would be as good as down were it not for Bignot's blunder.
Rangers kissed goodbye to their distant play-off hopes just as they were cruising to victory thanks to a first-half Gareth Ainsworth goal.
But battling Brighton slowly took advantage of Gallen's dismissal for throwing a punch in the 50th minute.
Bignot headed past his own keeper with ten minutes to go under only a touch of pressure from substitute striker Joe Gatting.
Brighton were all over the place from the start and were fortunate to stay on level terms for as long as they did.
QPR took the lead with some inevitability in the 13th minute when Ainsworth ghosted in from the right to head in a Lee Cook cross from the left.
Cook was a constant menace to Albion and he had nearly broken the deadlock as early as the third minute when he beat a couple of men on the edge of the box only to shoot narrowly wide.
Danish striker Marc Nygaard also had an opening, but he shot over the bar from close range.
Brighton could hardly break out of their own half and the pressure began to show in some of their tackling.
Lancashire referee Andy Leake booked defender Adam El-Abd and could have shown a few more yellow cards before half-time as the fouls began to flow.
But it was Rangers captain Gallen who really lost it by getting himself sent off five minutes into the second half.
Striker Gallen was tussling for the ball with Brighton defender Paul McShane and then swung a punch when the ball went away.
McShane theatrically hit the deck and eagle-eyed ref Leake quickly got out his red card, much to the annoyance of a furious Gallen.
McShane was then booed by QPR fans for the remainder of the game as the Brighton faithful finally found some hope to sing about amid their relegation woes.
Their only half chance, though, came in the form of a Colin Kazim-Richards free-kick that deflected wide for a corner.
That was until Gary Hart floated in an 80th minute cross and Bignot gifted Brighton an equaliser out of nothing.