Darlington came from behind after conceding a sloppy opening goal, but then the home side struck twice, and looked to be heading for their second victory of the season as the game moved into time added on.
But the visitors had other ideas and sub Steve Watkin grabbed a deserved equaliser, at the death to give Welshmen a well earned point.
The home side dominated, the opening 45 minutes, but failed to break through a Swansea defence that was superbly marshalled by captain Kris O'Leary.
Somewhat against the run of play the visitors took the lead with a goal out of the blue from defender David Smith in the 61st minute.
Darlington failed to clear a long throw, but there looked to be no danger when the loose ball fell to Smith 25 yards out, but the defender coolly curled the ball low into the far corner of Chris Porter's goal.
Darlington needed to respond quickly and they did in the 65th minute. Porter's long clearance was headed on by Barry Conlon and Ian Clark raced clear before firing low past Roger Freestone in the Swansea goal.
The home side took the lead in the 70th minute when captain Craig Liddle dived superbly to head in Neil Wainwright right-wing cross.
Three minutes later Darlington thought that they had been awarded a penalty when Wainwright was felled in the box. Referee Eddie Evans was unimpressed however and the Darlington midfielder was shown a yellow card for diving.
In the 79th minute Swansea made a double substitution when Neil Sharp and Watkin came into the fray.
Seven minutes from time Watkin almost grabbed an equalizer, but his acrobatic overhead kick struck an upright with Porter well beaten.
With time running out Darlington sat back and paid the price when Watkin was left free to head the equalizer from close range