The Rhinos, who received the League Leaders' Shield on their previous visit to the John Smith's Stadium, gave their all in the face of adversity, with no fewer than nine senior players watching from the sidelines.
But the Giants were good value for a win that will put them in good heart for when the two sides meet again in the sixth round of the Ladbrokes Challenge Cup at the same venue next Friday.
Leeds gave a debut to 17-year-old forward Cameron Smith, who became the sixth youngest player to make his Super League bow for them, while 19-year-old scrum-half Jordan Lilley did not deserve to be on the losing side.
It was a thrill-a-minute from the moment Huddersfield took a fifth-minute lead when second rower Ukuma Ta'ai took skipper Ryan Hinchcliffe's pass 10 metres out to power his way over the line after centre Aaron Murphy had dropped on a loose ball.
Danny Brough could not add the conversion but he tormented full-back Ashton Golding with a series of towering kicks and the visitors' defence was put under almost constant siege throughout the first quarter.
Prop Josh Johnson and winger Jermaine McGillvary both had tries disallowed by video referee Richard Silverwood and Leeds somehow hung on long enough for half-backs Lilley and Liam Sutcliffe to work their team back into the contest.
Lilley brought the scores level when he touched down Sutcliffe's grubber kick on 24 minutes, put his side in front with the conversion and extended the lead to 8-4 with a 31st-minute penalty.
Sutcliffe squandered a glorious chance to add to the lead when he burst clear and failed to make use of a two-man overlap then Huddersfield failed to make the most of a break by second rower Michael Lawrence and Hinchcliffe reached the line only to be held up on his back.
The frenetic nature of the game continued in the second half with the lead changing hands twice within eight minutes of the re-start.
Winger Gene Ormsby scored the first try of his loan spell from Warrington after Huddersfield had shifted the ball from right to left and Brough's touchline conversion put the Giants back in front.
Only four minutes later, Lilley's 50-metre break turned defence into attack, creating the position for second rower Josh Walters to burst over for his first try since scoring the winner in Leeds' Grand Final triumph last October.
Huddersfield went back in front on the hour when England winger McGillvary cut inside after taking Leroy Cudjoe's pass and wrong-footed the Leeds defence to score his 11th try of the season but the champions again struck back straight away, with skipper Rob Burrow forcing his way over from dummy half.
The Giants had the final say when Murphy brought the ball back inside and substitute Jake Connor charged onto his pass to score his side's fourth try and Brough kicked his third goal.