Guylain Ndumbu-Nsungu put them ahead on 48 minutes when he stole in unmarked to control Ryan Valentine's cross from the right flank before heading home past Brentford keeper Ben Hamer.
That calmed Darlington nerves and on 59 minutes Julian Joachim scored once of the best goals of the season.
He struck a brilliant shot into the top corner of the net after a flowing move which ended with Kevin Gall back-heeling the ball to the on-rushing Joachim, who hit it first time from 20 yards.
Brentford sub Reuben Reid set up a nervy finish for Darlington by scoring from close range on 82 minutes with his side's only clear opening of the half.
But Darlington roared back on the attack and sub Pawel Abbott added a third on 89 minutes after Hamer fumbled a cross from Neil Wainwright.
It was just reward for Darlington's dominance, but they could have paid for missed chances when 2-0 up.
Michael Cummins, Wainwright and Bryan Hodge all missed opportunities to kill Brentford off.
It was in stark contrast to a dire first half in which neither side got to grips with the swirling wind or each other.
Darlington's only shot on target was a tame effort from Ben Parker, who was making his debut.
Brentford faired marginally better with Robert Milsom's 37th minute cross finding the head of Nathan Elder, whose looping header was saved by David Stockdale.
Then on 43 minutes, Alan Connell broke clear. Stockdale saved at his feet and Glenn Poole was unable to turn the loose ball in as the defence quickly regrouped.
It was clear that Darlington's 4-3-3 formation was not working and they switched to 4-4-2 in the second half, with the tactical change paying immediate dividends.
They have struggled to win home games lately and by romping home this time their confidence will be boosted for the promotion push.
But for Brentford, the play-offs are now a distant dream after their revival has hit the buffers with three successive defeats in a week they will want to forget.
They will have to quickly rediscover their form if they are to reach the top seven.