The Whites went in front twice but were pegged back by their South Wales visitors and ultimately held for a second consecutive Championship match.
Brenden Aaronson opened the scoring on 35 seconds but Leeds did not appear at their sharpest throughout the first half. Harry Darling pounced upon a second half Illan Meslier error to level proceedings before late substitute Willy Gnonto put United back in the lead.
However, Swans striker Zan Vipotnik had the final say, striking in the 96th minute to ensure spoils were shared.
13. Largie Ramazani (sub): 5/10
We saw some good - his fight, willingness to tackle and a little bit of skill - and some bad - his careless giving away of the ball in a dangerous area. | Martin Rickett/PA Wire
14. Ao Tanaka (sub): 5/10
Passed the ball straight out for the corner before the one Meslier dropped. Unable to make a challenge ahead of the second goal. Wasn't anywhere near his standard. Photo: George Wood
15. Mateo Joseph (sub): 5/10
It was his poor touch that gave the ball to the Swans ahead of the second goal. Didn't really add much when coming on. Photo: George Wood
16. Junior Firpo (sub): 6/10
Added a bit of physicality and urgency at least. Won headers. Tried to get forward and link up. Photo: Bruce Rollinson
17. Referee - Ben Toner: 6/10
A young referee and inexperienced at this level and it threatened to get away from him later on but got the penalty right. A few mistakes for either side. Used his cards well enough in the main. | Getty Images