The point was Carlisle's first draw at home this season but stretched their winless streak against the Quakers to 14 games.
The home side dominated in the first half but, despite being almost camped in their opposition's half, clear chances were few and far between.
Brendan McGill went closest with a firm header that was tipped wide by the hand of Bertrand Bossu.
On the half-hour United's Danny Livesey was held down in the box by Shelton Martis and to the horror of the visiting fans, and the surprise even of the Carlisle players, referee Mike Jones pointed at the spot.
Chris Lumsdon calmly stroked home the penalty as the Darlington players continued to debate the award.
But just eight minutes later the Quakers were celebrating when Simon Johnson converted their first chance of the match.
Carlos Logan hit a deep cross to the far post and the unmarked Johnson stooped to head past the flapping Keiren Westwood.
The visitors came out fighting in the second half and Carlos Logan forced a good save from Westwood at the keeper's near post.
With neither team looking likely to force a clincher, the Cumbrians brought on winger Simon Hackney and with a bit more luck, he could have won the game.
Chris Billy tricked his way into the box and crossed to the back post, only for Hackney to see his diving header scrambled off the line by defender Brian Close.
Carlisle's top scorer Karl Hawley then spun away from his marker, but could only blast his eight-yard shot straight at Bossu.
With the hosts pushing for victory Darlington made one final attack.
Guylain Ndumbu-Nsungu burst forward and laid the ball off to the unmarked Jonjo Dickman, but his first-time shot trickled agonisingly wide.
With the visitors finishing the stronger, United's biggest crowd of the season will have gone home just happy that their side's unbeaten run was stretched to five games.