Despite a far from convincing performance by promotion-chasing Darlington, the Quakers eventually gained another vital three points.
The visitors can count themselves unlucky after a sterling second-half performance that should have brought some reward.
The home side took the lead after only 11 minutes when the Barnet defence failed to clear a long throw from home defender Paul Mayo.
The defensive clearance fell to Julian Joachim, on the edge of the area, and his low drive flew in to the bottom corner of the net beyond the despairing dive of Bees keeper Rob Beckwith.
The early goal should have been a springboard for the home side who have only tasted defeat on home soil once so far this season.
But despite further chances falling to Bryan Hodge in the 16th minute and defender Alan White nine minutes later, the game eventually turned on a refereeing decision on the half-hour mark.
White man-handled striker Cliff Akurang to the ground inside the area and referee Phil Joslin had no hesitation in pointing to the spot. What was confusing was the yellow card shown to White when a red should have been the outcome.
To rub salt into the wounds Darlington keeper David Stockdale then proceeded to save teenager Josh Wright's penalty kick.
The visitors took the game to the home side after the break, but they failed to take any of the chances that fell their way in a commanding second 45 minutes for Barnet.
In the 51st minute an equaliser looked certain when Akurang broke clear until Stockdale again came to his side's rescue.
In the 65th minute Wright again went close for the visitors with a shot from the edge of the area that went inches over the crossbar and then, five minutes later, defender Joe Devera tried his luck from 25 yards out with a shot that almost scraped the crossbar.
With 15 minutes left Barnet captain Ismail Yakubu saw his header fly over the bar and Darlington seemed to take heart from the near miss as they began to play some good football again as the match came to a conclusion.
Five minutes from time Joachim raced away and fed defender Ryan Valentine who wasted a glorious opportunity to settle the match.
