Marsh-Brown, on loan from Fulham, slotted the Dons' opener shortly after the break, but Lewis Grabban levelled for Brentford two minutes later, maintaining Nicky Forster's unbeaten record as Bees caretaker boss.
Brentford missed three glorious chances to open the scoring in the first half as they carved a makeshift Dons' defence apart at will.
The Dons improved after the break and the impressive Marsh-Brown put them ahead three minutes after the restart, slotting in Luke Chadwick's low cross from close range.
But Grabban equalised for Brentford two minutes later when he raced clear on to Leon Legge's pass and drilled a low shot inside the far post beyond the fingertips of Martin.
The Bees piled forward late on, Marcus Bean lashing a 25-yard strike against the crossbar and Gary Alexander heading the rebound over, while Sean O'Hanlon headed just wide for the Dons in the closing seconds.