Hull KR overcame a disastrous start to comfortably book their place in the last eight of the Carnegie Challenge Cup in an entertaining fifth-round tie at Craven Park.
Huddersfield, the 2006 runners-up, made a dream start by racing into a 12-0 lead after 17 minutes but finished a well-beaten side and, with just two wins from their last 11 matches, this result can only increase the pressure on coach Jon Sharp.
It was 22-22 until Rovers winger Peter Fox scored the second of his two tries on 53 minutes but two late tries emphasised the home side's superiority.
Yet a shock had been on the cards when the Giants ran in two tries in four minutes, with New Zealand Test centre Paul Whatuira touching down a kick from scrum-half Luke Robinson and acting captain Ryan Hudson finishing off a break by loose forward Steve Snitch.
Robinson added both conversions to put the visitors 12-0 ahead but Huddersfield were unable to hold onto a 16-point lead in the Super League against Warrington a week earlier and showed little sign of sterner resistance on Sunday.
Scott Murrell, who is filling in at scrum-half until the arrival of Australian Michael Dobson, sparked the Rovers fightback, stretching out of a three-man tackle to plant the ball on the line after 21 minutes.
Hull KR's other first-half tries all stemmed from kicks, with Huddersfield full-back Rod Jensen proving a liability under the high ball.
Left winger Daniel Fitzhenry pounced on Ben Cockayne's kick to the corner, right winger Peter Fox crossed in the other corner after Jensen fumbled Cooke's towering 'bomb' and full-back Shaun Briscoe followed up Murrell's grubber kick to get the vital touch.
Sharp eased the shell-shocked Jensen out of the firing line, switching Shane Elford to full-back, while Roversoo made a change at full-back, Briscoe making way for Cockayne after taking a knock to his head in the act of scoring.
The Giants briefly drew level with two tries in the first eight minutes of the second half with Whatuira taking advantage of a loose ball to go 40 metres to the line for his second try and right winger Martin Aspinwall making the most of a remarkable offload from a four-man tackle to touch down at the corner.
Substitute hooker Tom Hemingway kicked one of the conversions to tie the scores at 22-22 but Huddersfield's fragile defence cracked twice in four minutes as the game finally swung the way of the home side.
Cooke, Ben Galea and Chev Walker combined to get Fox over for his second try and captain Mick Vella made the most of some weak tackling to grab his side's sixth try.
Huddersfield battled to the end, with stand-off Kevin Brown slicing open the Rovers defence only to lose his footing while man of the match Clint Newton pulled off a flying tackle to deny Aspinwall a second try.
The Robins then demonstrated their superior finishing, with substitute Chris Chester and hooker Ben Fisher grabbing late tries and Cooke taking his goal tally to five from eight attempts.