Super League elimination play-off highlights:
Date: Sunday 19 September Coverage: BBC Two from 1700-1745 BST, and on the BBC Sport website (UK only)
Warrington (0) 22
Tries: Higham 2, Hicks 2 Goals: Westwood 3
Huddersfield (23) 34
Tries: Wild, Gilmour, Kirmond, Brown, Cudjoe Goals: B Hodgson 6
Drop Goal: Brough 2
Cudjoe was among the Super League's Top 10 try scorers this season with 22
Leroy Cudjoe was again a last-gasp hero for Huddersfield as his 90-metre interception try saw the Giants through to the play-off semi-finals.
Huddersfield's famous victory at the Halliwell Jones really ought to have been sewn up by half-time, after scoring four tries to lead 23-0.
But Wolves hit back with tries apiece for Mickey Higham and Chris Hicks.
And it needed a nerve-settling drop goal from man of the match Danny Brough before Cudjoe sealed victory.
That was Brough's second drop of the night, having also stuck one over in the final seconds of the first half, to put the seal on tries by Stephen Wild, Lee Gilmour, Danny Kirmind and Kevin Brown.
And, although they were outscored four tries to one as the Wolves roared back after the break, Nathan Brown's battlers hung onto the rollercoaster to book a first-ever play-offs semi-final - just a week on from being 10 minutes away from an upset themselves, at the hands of Crusaders.
Warrington had won their last four meetings with Nathan Brown's men, including a 60-4 hammering at the Galpharm in May on their way to a successful defence of the Challenge Cup they won against the Giants a year ago.
But they were in for a rude awakening against a Giants side full of confidence after winning their last six matches.
Former Huddersfield coach Tony Smith was forced to make a late change when loose forward Ben Harrison tore his hamstring in the warm-up - and had to be replaced by Vinnie Anderson.
And the Wolves were further stunned when it took the Giants just two minutes to open the scoring.
They were gifted a perfect attacking position when Warrington full-back Richie Mathers knocked on on the first tackle on his own 20-metre line - and Huddersfield loose forward Stephen Wild took an inside pass from stand-off Kevin Brown to go in for the first try.
Danny Brough then set up a second try on 14 minutes for second rower Danny Kirmond, on his first start of the year.
Brett Hodgson kicked both goals to earn a 12-0 lead and the Huddersfield fans were in dreamland midway through the first half when centre Gilmour dribbled ahead after getting to Brett Hodgson's grubber kick to score try number three.
Warrington did show signs of putting their game together, largely through the efforts of wily stand-off Lee Briers, but Huddersfield's scrambling defence was superb. And the Yorkshiremen extended their lead on 33 minutes when Brown forced his way over at the corner for a fourth try.
Hodgson missed with that kick, but Brough made partial amends when he slotted over a 40-metre drop goal on the stroke of half-time.
After being booed off at the break, Warrington urgently needed a rapid response at the start of the second half - and they got one when substitute Mickey Higham found a way in just four minutes after the restart, Ben Westwood adding the goal.
Hodgson then missed his second kick of night before this time getting it right with a second penalty attempt to steer Huddersfield into a 25-6 lead 13 minutes into the second half.
But the Wolves again moved a little closer just before the hour when fit-again winger Hicks went in for his 31st try of the campaign, Westwood missing with the kick.
And there was genuine cause for concern when Higham added a second try, Westwood landing an impressive conversion to make it 25-16.
Again the Giants responded with a Hodgson penalty, but when Hicks went in for his second try, Westwood once more doing the business with the boot, there was now only one score between the two sides.
The Giants were to have the last word, however.
Brough's drop stretched that gap to six points again and, with the Wolves now on the attack, needing a converted try to take the game into extra time, Cudjoe burst clear to settle it.
Warrington coach Tony Smith said:
"I'm glad we made a game of it in the second half. I'm sure it was an exciting finish for the fans but unfortunately we left ourselves way too much to do.
"I've got to give credit to Huddersfield. Their tactics in the first half hurt us. We didn't cope with them very well.
"They've been on the back end of a few scorelines against us so all credit to Nathan for turning his troops around."
Huddersfield coach Nathan Brown said:
"There are a lot of people out there who probably thought there wasn't a game to be played today.
"If you believed all the experts, St Helens were going to pick Warrington. It was like there was no contest today.
"We didn't play great last week but, apart from that, our form has been pretty reasonable.
"We've got good players coming into form at the right time of the year and our squad is pretty healthy."
Warrington: Mathers, Hicks, King, Atkins, Riley, Briers, Monaghan, Morley, Clarke, Carvell, L Anderson, Westwood, V Anderson.
Replacements: Bridge, Higham, Wood, Solomona.
Huddersfield: B Hodgson, Cudjoe, Lawrence, Gilmour, D Hodgson, Brown, Robinson, Mason, Brough, Griffin, Kirmond, Fa'alogo, Wild.
Replacements: Crabtree, Lunt, Faiumu, Patrick.
Referee: Phil Bentham (Warrington).