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.
1. Illan Meslier: 4/10
Saved a penalty, saved shots, kicked it well and was heading for an 8 until he dropped a corner and handed Swansea a gift. The second goal was from such an acute angle that he had to do better. | Martin Rickett/PA Wire
2. Jayden Bogle: 6/10
Involved in the opener but wasn't at his best. Leeds' lack of fluidity hampered his ability to get forward. Drove Leeds up the pitch a few times in the second half but lacked composure. | Martin Rickett/PA Wire
3. Pascal Struijk: 6/10
Unable to help dictate with his passing or get the left flank going. Some careless stuff on the ball and was nutmegged ahead of the second. | Martin Rickett/PA Wire
4. Joe Rodon: 6/10
Guilty of a clumsy challenge for the penalty, having done well to get into position to cover. Passing to feet was decent but when he went long it wasn't always great. | Martin Rickett/PA Wire
5. Sam Byram: 6/10
Some strong challenges, popped up in a couple of good positions but couldn't find the target or a telling cross. | Martin Rickett/PA Wire
6. Ethan Ampadu: 5/10
A rusty performance. Couldn't quite get his rhythm. Didn't have the time he wanted on the ball and when he did his decision-making or execution was off. Took a yellow but probably had to. | Martin Rickett/PA Wire