Nathan Austin and Jordan McGhee had both gone close for the Bairns before Queens stunned the visitors with two quickfire goals.
Stephen Dobbie was first to strike when he charged down a Robbie Thomson clearance before rolling the ball into the unguarded net. Three minutes later Dobbie turned provider with a neat flick which released Lyndon Dykes to score from an acute angle.
The Doonhamers looked in total command when Darren Brownlie rose above the Bairns defence to head Connor Murray’s corner low into the net.
However, Falkirk refused to throw in the towel and grabbed a lifeline when Joe McKee netted direct from a free-kick.
They then raised hopes of an improbable comeback when Jordan McGhee headed Dunne’s cross beyond Martin, only for Derek Lyle’s breakaway goal to settle the match in stoppage time.