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.
7. Joe Rothwell: 6/10
Flitted in and out of it. At times looked like he would be able to make things happen. Some decent set-piece deliveries. | Martin Rickett/PA Wire
8. Dan James: 7/10
Started well, faded for a spell and then came back into it in a big way to really threaten Swansea on the right. Unlucky not to score. | Martin Rickett/PA Wire
9. Manor Solomon: 6/10
A couple of bright moments in possession but didn't take the game by the scruff of the neck as he's capable of doing. | Martin Rickett/PA Wire
10. Brenden Aaronson: 5/10
Got his goal inside a minute to lift some of the pressure. Started brightly but started to give away too many free-kicks and the ball on occasions. Made a nice chance for Piroe second half. | Martin Rickett/PA Wire
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11. Joel Piroe: 5/10
Could and should have scored. Finishing wasn't there but he was in the right place. A couple of nice bits of link-up play but not enough of a factor at times. | Getty Images
12. Willy Gnonto (sub): N/A
Thrown on for the last five and time added on. Instant impact with the composure and finish for the second goal. | Martin Rickett/PA Wire