Jesse Marsch's side went ahead in the 56th minute through an ice-cool penalty from Rodrigo which was awarded after Crysencio Summerville was fouled.
Palace, though, equalised 11 minutes later through Jean-Philippe Mateta who was left with a tap-in from a rapid Eagles break from a Whites corner.
Leeds were also hit with a fresh injury blow as the Whites lost summer signing Luis Sinisterra to a hamstring injury.
In a niggly and ill-tempered contest featuring several yellow cards, Adam Forshaw was also withdrawn after just 33 minutes after tweaking his knee.
Graham Smyth, the YEP’s chief football writer, hands out the scores from the Friday contest at the Optus Stadium in Perth.
7. Adam Forshaw
6 - Off injured in the first half. Hadn't really put a foot wrong, looked after the ball better than some team-mates. Photo: Bradley Kanaris
8. Jack Harrison
7 - Some beautiful examples of that first touch he possesses, not too many deliveries to match it. Spent time at left-back. Worked tirelessly. Photo: Albert Perez
9. Luis Sinisterra
N/A - Limped off after just 12 minutes. Hasn't got going yet in pre-season. Big worry for Leeds if it is his hamstring. Photo: Paul Kane
10. Brenden Aaronson
6 - Buzzed around, tried to get on the ball. His work-rate is going to be a feature for Leeds but he looked lively in possession. Photo: Bradley Kanaris
11. Patrick Bamford
6 - Came close to a first half goal, showed skill, hold up play, but still a little rusty. Photo: Paul Kane
12. Rodrigo (sub)
5 - Took the penalty well, there were a couple of nice bits of link-up play but some not so good stuff in possession too. Photo: Chris Hyde