The picture looks clearer after crucial wins for Hull KR, Salford Red Devils and Warrington Wolves that leave the chasing pack four points behind.
Huddersfield held their nerve to move level on points with the Rhinos in the final match of the round but seemingly need to win all their remaining games and are relying on some help elsewhere.
The season was on the line for both teams at the John Smith's Stadium and the clash had a cup tie feel.
In the end, Leeds gave themselves too much to do after conceding three scruffy tries in a first half disrupted by a long stoppage following a neck injury sustained by James Bentley.
The Rhinos, who lost four players from the team that beat Warrington in their previous outing including Nene Macdonald and David Fusitu'a, rallied before the interval but were kept scoreless in the second half on their way to a damaging defeat.
Barring a minor miracle, there are only four games remaining of a forgettable season for both sides.
The inquests will come later but the rival camps will spend the coming days picking the bones out of a breathless game that had talking points galore.
The tone was set in the opening minute when Sam Walters went close on the final play of the first set.
Referee Marcus Griffiths – a central figure throughout a pulsating affair – brought play back for a late hit that forced Harry Newman off for a HIA against his wishes.
The centre insisted he was fine to continue but he had to go off in line with the concussion protocols and returned to find Huddersfield in control.
The Giants broke the deadlock in the 10th minute when Jake Connor gave Sam Halsall a simple finish in the corner after Olly Russell's pass had gone to ground.
A Bentley ball steal had given Huddersfield the field position to find the breakthrough and his afternoon was soon over following a collision with Connor competing for a high kick.
The Leeds back-rower received treatment on the field for the best part of 15 minutes before being taken straight to hospital for further assessment, Newman his replacement after being given the all-clear to return.
To compound matters for the visitors, Huddersfield were awarded a penalty and scored at the end of the set in controversial fashion.
Players on both sides stopped expecting a handover with the tackle on Kevin Naiqama seemingly complete but the Fijian centre reached out to touch down and the try was signed off by the officials.
The momentum was with the Giants and Leeds could not turn the tide, Tui Lolohea finishing just before the dead-ball line after Ash Handley fumbled his kick under pressure from Esan Marsters.
The Rhinos were aggrieved with the contact in the air but their protests were waved away.
Although Russell hit the post from the tee, Leeds were staring down the barrel of a season-ending defeat at 16-0.
But the Rhinos are at their best with their backs against the wall and they found a route back into the game.
Rohan Smith's men had some luck along the way, Marsters adjudged to have lost the ball going for the line in a first-half turning point.
Leeds made the most of the reprieve to score at the other end through Luke Hooley from a perfectly executed set move.
Aidan Sezer found Walters close to the line and he tipped back inside for Hooley to finish.
Rhyse Martin added the extras to reduce the deficit with six minutes to go until the break, which was enough time for the visitors to land another blow – but not before benefiting from another slice of fortune.
Marsters – playing out of position on the wing – was guilty of another poor finish in the corner and Sam Hewitt was sin-binned for delaying the restart, just seconds after entering the field.
In the final minute of the half, Martin forced a drop-out with a neat kick in behind and Leeds scored with seven seconds remaining.
The impressive Sam Lisone skittled a couple of would-be tacklers on Huddersfield's right edge and offloaded to Ash Handley who did the rest.
After seeing Martin add a nerveless touchline conversion, the Rhinos ran in at half-time with a steely look in their eyes.
But ultimately the interval came at a bad time for Leeds who could not find the same rhythm in the final 40 minutes.
The Rhinos carved Huddersfield open on several occasions in an increasingly scrappy contest but lacked the composure to finish the opportunities.
Cameron Smith, who led from the front once again for Leeds, ran into open space after storming through the middle of the Giants. However, he could only find Lisone in support and he was dragged down 10 metres from the line.
Huddersfield were unhappy with the contact from Lisone that flattened Halsall in the build-up but the Rhinos were allowed to continue after a delay and went close when Hooley's pass dropped short of Handley with the winger wide open.
Connor swung the momentum Huddersfield's way with a 40/20 and Will Pryce brought some calm to proceedings when he knocked over a penalty to make it 18-12 after Leeds were caught offside in the next set.
It had the look of a curious decision at the time yet it proved to be a match-winning call.
The Rhinos had their moments in the remaining 25 minutes but they were largely held at arm's length.
Leeds knew their race was run when Connor kicked a contentious drop goal in the closing stages and Pryce quickly added a second penalty after the visitors were penalised for obstruction on a kick return.
The Huddersfield fans serenaded the travelling supporters with 'Leeds are falling apart again' as they exited the away end but there is little to suggest either side will make the play-offs.
Huddersfield Giants: Connor, Marsters, Naiqama, Bibby, Halsall, Russell, Lolohea, Hill, Milner, Ashworth, Cudjoe, McQueen, Yates. Substitutes: Pryce, Greenwood, Ikahihifo, Hewitt.
Leeds Rhinos: Hooley, Olpherts, Roberts, Newman, Handley, Martin, Sezer, Oledzki, O'Connor, Holroyd, Bentley, Walters, Smith. Substitutes: Donaldson, Lisone, Gannon, Ruan.
Referee: Marcus Griffiths.