Heffernan's big chance came after Darren Pratley had pushed James Hayter in a goal-mouth melee.
But he hit his spot-kick too close to on-loan Dimi Konstantopoulos, who blocked the shot and when Heffernan followed up he headed into the keeper's arms.
The failed opportunity stretched Rovers' run to 11 games without a victory, but they did manage to pick up only their second point during that period thanks to a battling display.
Swansea began as if they intended to play Doncaster off the park in a whirlwind start which had the home side struggling to cope with their pace and skill.
But Rovers weathered the early storm and came into the game to give the Welshmen a taste of their own medicine with some determining attacking soccer.
But despite the enterprise and skilful approach work from both sides, they badly lacked a cutting edge to break the deadlock.
Jason Price went close several times for Rovers against his former club and hit an angled 20-yarder inches wide in the 29th minute.
Leon Britton hit the sidenetting at the other end just before the interval, before Lewis Guy missed a great opportunity for the home side when he fired widely off target after being put clean through with the only the keeper to beat.
Price volleyed just wide again from the edge of the box in the 55th minute, before Jason Scotland had a shot on the turn comfortably saved four minutes later as play continued to switch quickly from end to end.
And the ever dangerous Price had a 20-yards snapshot deflected just wide in the 59th minute as Rovers continued to battle to find an opening.
But when the opportunity came from the penalty spot in the closing stages, Heffernan failed miserably to seize the chance, but overall a draw was a fair result between two capable sides who only lacked the finishing touch.