The home side went in front early on thanks to some clever work from Carl Ablett, before Adam Cuthbertson notched Leeds's second try in the 23rd minute to push the hosts further in front at 12-0.
Jamie Ellis returned for Huddersfield in the 32nd minute to claw some points back after Kevin Sinfield had originally helped to kick Leeds further into the lead.
The Giants gave themselves a route back into the game just before the break thanks to Joe Wardle, who touched down to leave the scores at 18-12 going into the interval.
Tom Briscoe was on the mark straight after half time as he put Leeds further in front, but the Giants weren't done yet as some neat offensive play from Kyle Wood and Brett Ferres put the away side into a 24-22 advantage with just over 10 minutes to go.
Unfortunately for Huddersfield, they had not counted on the heroics of Paul Aiton, who touched down in the 74th minute to build on good work laid down by Sinfield to give Leeds a slender comeback win.