Rhinos led by 10 points with two minutes remaining, but the visitors scored back-to-back tries to level the scores at 20-20 and neither team could find a golden-point winner in extra-time.
The 10 added minutes wasn't what either side wanted at the start of the Easter fixture pile-up and Rhinos suffered one major injury blow.
The performance for all but the final few minutes of normal time will, though, give Leeds something to build on going into Monday's derby at Castleford Tigers.
Here's how the players rated.
7. Liam Sutcliffe
8: Played two roles, scored a good try and a strong effort to get out of goal in extra-time was vital. Photo: Bruce Rollinson
8. Mikolaj Oledzki
8: Powerful effort at the heart of the pack. Picture by SWpix.com. Photo: Swpix.com
9. Kruise Leeming
8: Had to switch into the halves after Walker's injury, but set a good lead. Picture by Allan Mckenzie/SWpix.com. Photo: Allan McKenzie/SWpix.com
10. Matt Prior
7: On and off, solid stints. Picture by Allan McKenzie/SWpix.com. Photo: Allan McKenzie/SWpix.com
11. James Bentley
8: His best game for Leeds, aggressive and took some stopping. Picture by Bruce Rollinson. Photo: Bruce Rollinson
12. Rhyse Martin
8: Scored a fine try - if only his second conversion attempt had gone over, rather than hitting a post. Picture by Bruce Rollinson. Photo: Bruce Rollinson