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.
1. Jack Walker
7: The full-back was going well before picking up what appeared to be a serious hamstring injury. Photo: Bruce Rollinson
2. Liam Tindall
7: One outstanding run and worked hard, but had to as Giants attacked his side. Photo: Bruce Rollinson
3. Tom Briscoe
Was tested on defence, but ran the ball back strongly 7 Photo: Steve Riding
4. Alex Mellor
7: Played out of position on his return to the side and did a steady job. Photo: Alex Whitehead/SWpix.com
5. Ash Handley
7: No real scoring chances, though a strong run set up one try. Photo: Alex Whitehead/SWpix.com
6. Blake Austin
8: Kick out on the full was costly, however, he played well and his pass for Rhyse Martin's try was outstanding. Photo: Alex Whitehead/SWpix.com