Brentford had the better of the chances but the lack of a clinical finisher in front of goal may end up costing them this season, while Darlo seemed to be able to score at will despite not being at their best.
Terry Butcher's men got off to the better start with forwards Lee Thorpe and the impressive Charlie Ide linking well upfront.
The first attack from the home side saw Ide knock the ball down well into the path of Sammy Moore on the edge of the box, but he failed to keep his shot on target.
Moore went close again minutes later with a curling free-kick which was heading into the top corner but for the goal-line header from Neil Austin.
In the 16th minute Brentford's failure to convert their chances was punished as Kevin O'Connor carelessly tripped Tommy Wright on the edge of the box and referee Mike Thorpe had no hesitation in pointing to the spot.
Clarke Keltie stepped and coolly slotted the ball down the middle past a helpless Simon Brown to give the Quakers the lead against the run of play.
The goal kicked the visitors into action and they started to play with more determination with former Aston Villa striker Julian Joachim at the heart of everything that was good about Darlington.
Inevitably it was Joachim who was involved in creating Darlington's second which wrapped up the points.
He picked up the ball on the right flank and played a low ball across the area for Gregg Blundell who crossed for Wright to head home from close range.
The second half started much the same as the first with Brentford on top.
And yet again it was Moore who was carving out the best chances. He drilled a right-footed shot from the edge of the area which keeper David Stockdale, at full stretch, tipped round the post.
Substitute Ryan Dickson created the best chance for the hosts when he made a brilliant run down the left wing and crossed for Ide, but the striker's shot was blocked on the line by Alan White.
Brentford will need to improve their finishing if they are to see an upturn in their results while Darlington are putting together a good promotion charge.