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.
13. Cameron Smith
7: Not much joy on attack, but worked hard defensively. Picture by Bruce Rollinson. Photo: Bruce Rollinson
14. James Donaldson (sub)
7: Limited game time, but put himself about. Picture by Allan McKenzie/SWpix.com. Photo: Allan McKenzie/SWpix.com
15. Morgan Gannon (sub)
8: Morgan Gannon. Big contribution, scored a terrific try. Picture by Bruce Rollinson. Photo: Bruce Rollinson
17. Zane Tetevano (sub)
7: Decent return from suspension, ran hard. Picture by Tony Johsnon. Photo: Tony Johnson
18. Huddersfield Giants
Tui Lolohea 6, Jermain McGillvary 7, Leroy Cudjoe 7, Ricky Leutele 7, Innes Senior 7, Jack Cogger 6, Theo Fages 7, Chris Hill 7, Danny Levi 6, Owen Trout 6, Josh Jones 5, Chris McQueen 6, Luke Yates 7. Subs Oliver Wilson 5, Matty English 5, Joe Greenwood 7, Ashton Golding 6. Picture by Bruce Rollinson. Photo: Bruce Rollinson