Only the brilliance of goalkeepers Paul Smith and Dorus de Vries kept the game goalless, particularly during a first half that was packed full of chances.
The sides cancelled each other out after the break with a last-minute header from Luke Chambers the closest either came to breaking the deadlock.
But, while a draw was a fair result from an entertaining encounter, it will be Roberto Martinez's side who will wake up the happiest after maintaining their 11 point lead over the Reds.
Swansea were the first to threaten as winger Paul Anderson let fly from just inside the box but saw his angled shot charged down.
It took Forest longer to build momentum, although Kris Commons sent a low effort flashing across the face of goal and wide and Grant Holt saw a looping header drop over.
It was a header at the other end from defender Wes Morgan that caused chaos for Forest.
While attempting to steer the ball back to Smith, he instead headed the ball beyond the advancing keeper and ended up sliding to clear the ball off his own goalline.
And with Swansea starting the stronger, it was Smith who was called into action again, this time as he threw himself at full-stretch to his right to hold a skimming effort from Andy Robinson.
But Morgan almost made amends at the other end as, twice in the space of the minute, he rose to connect with Commons' corners only to head narrowly wide on both occasions.
De Vries had to be on his toes when teenager Matt Thornhill flicked the ball into the box to the feet of Holt, whose prodded shot on the turn tested the keeper's reactions to the limit.
Swansea twice came close as Smith produced smart saves of his own to deny Guillem Bauza and Robinson.
But this was becoming an end-to-end affair with Thornhill again bringing the best from de Vries with a powerful driven shot from 12 yards, while the keeper also did well to get his body behind an angled shot from Nathan Tyson as the home side pushed for an opening goal.
The first half finished with Swansea in control as Robinson bent a spectacular free-kick narrowly wide.
But following a first period that was brimming with opportunity, the second became more of a tactical battle as Forest prevented Swansea from maintaining their flowing football and in doing so lost any attacking momentum of their own.
Holt came close to breaking the deadlock with a close-range header that de Vries plucked from the air with confidence.
A Chambers header almost snatched victory for Forest in injury time with the Swansea keeper saving again.