They are heading for relegation without a fight after slumping to their 12th loss on home soil this season.
One more Arena defeat and Quakers will equal the club record for home league losses in a single season, recorded in the early 1990s.
However, today's crowd of 1,463 was not only the lowest in seven seasons at the stadium, but the club's smallest league attendance since February 1993.
The result represented the Bees' first win at the Arena in five attempts, while it was the third time Darlington have lost to the Londoners this season as they also win an FA Cup tie at Underhill in November.
This time the Bees scored all three goals as the hosts' solitary strike was handed to them via an own goal.
Defender Gary Breen, a former Republic of Ireland team-mate of Darlington manager Steve Staunton, inadvertently put the ball into his own net early in the second half.
But by that stage Staunton's relegation-bound side were already 2-0 behind thanks to two first half strikes.
Quakers were slow to react at a corner which allowed Bees midfielder Dave Livermore to volley home the first goal on 23 minutes, and Albert Adomah lashed home the second nine minutes later.
After receiving the ball from the left, he was allowed far too much space on the edge of Quakers' penalty area from where the Barnet winger struck a powerful effort beyond keeper Shane Redmond.
There appeared to be no way back for shot-shy Darlington who had handed Noel Whelan a surprise start.
The former Middlesbrough striker has been troubled with a hamstring strain ever since signing in October but he was in the line-up today for his third appearance.
But he missed Quakers' first chance, volleying over from close-range after collecting a Tadhg Purcell pass.
Darlington's first effort on target did not come until Gary Smith struck a low shot from distance just before the break.
Keeper Jake Cole had little trouble in dealing with the effort, but Cole should have been given no chance when Gareth Waite was presented with a one-on-one in first half injury time.
The former Spennymoor midfielder latched on to a Tadhg Purcell through-ball but Waite's weak effort allowed Cole to save.
A goal then would have perhaps given Quakers the inspiration needed to mount a comeback, though they finally pulled one back n 57 minutes.
Winger Chris Moore, making his first start for the club after joining from Whitley Bay, sent in a right-wing cross that Breen deflected past Cole.
With Staunton wary of Whelan exerting himself, immediately after the goal the striker was replaced by Mor Diop but the next chance fell to fellow sub Josh Gray.
It was a superb chance too. Moore crossed from the right to the far post where Purcell pulled the ball back to Gray but his weak effort was blocked on line by Cameroon-born defender Clovis Kamdjo.
That proved to be the last chance for sometime as Barnet, content to sit on their lead, showed little interest in going forward while Staunton's side struggled in front of goal.
Ian Miller headed well wide at a Moore corner on 70 minutes and thereafter but there was no sense of urgency and little fight among a side seemingly resigned to their fate.
In the dying seconds Purcell headed wide and there were shouts for a Darlington penalty after Joe Devera appeared to handle.
With Cheltenham Town gaining a point, Quakers are now 19 points off third-bottom and all that remains to be settled this season is the date on which relegation is confirmed.
Goals: Livermore (23, 0-1), Adomah (32, 0-2); Breen OG (57, 1-2)
Bookings: Miller (79, foul)
Referee: Chris Sarginson
Darlington (4-4-2): Redmond; Madden, White, Miller, Milne; Moore, G Smith, Waite, Chisholm (Gray 45); Purcell, Whelan (Diop 58 (Main 90)). Subs (not used): Liversedge (gk), Groves, Mulligan, McReady
Barnet (4-5-1): Cole; Devera, Breen, Kamdjo, Lockwood; Adomah, M Hyde, Hughes, Livermore, Jarrett (Gillett 73); O'Flynn (J Hyde 90). Subs (not used): Carpenter (gk), Deverdics, O'Neill, Wright, Upson