The striker headed in Simon Johnson's cross 15 minutes from time to stretch the Quakers' unbeaten run to four matches and heap pressure on the Stags' under-fire player-manager Carlton Palmer.
Palmer, who threatened to quit after defeat the previous weekend, has now seen his side take just two points from five league outings.
The Stags, who had conceded 10 goals in those previous four matches and already lost two home games, failed to put away a couple of early half chances, Alex John-Baptiste heading Gus Uhlenbeek's corner wide and Simon Brown failing to convert another cross from the experienced full-back.
Quakers boss Dave Hodgson kept faith with reserve keeper Bertrand Bossu for a fifth successive game even though first choice Sam Russell had recovered from injury.
But it was the Frenchman's opposite number, veteran Kevin Pressman, who had to make the first save as he superbly punched away Akpo Sodje's close-range header.
And that stop proved vital in the ninth minute when the Stags took the lead against the run of play.
Richie Barker's acrobatic overhead kick narrowly failed to connect with a third Uhlenbeek cross but the ball ran kindly for Brown to stab in from seven yards.
The match only went ahead after several inspections of the sodden pitch following torrential rain and it was the Stags who adjusted better to the conditions.
But when Darlington eventually fought back they deservedly levelled in the 39th minute from Carlos Logan's free-kick.
Pressman again denied Sodje from point blank range but the recalled Matt Clarke cleverly back heeled the ball over the line.
Brown should have restored the Stags' lead two minutes into the second half, but after being put clear by Barker's neat flick, the striker crashed his final shot into the side netting.
However, in the 64th minute. he was gifted his second when Bossu made a mess of clearing Joey Hutchinson's back pass and Brown slotted into an empty net.