A sudden-death, golden-point drop-goal from Lee Briers saw Warrington snatch a place in the Challenge Cup semi-finals at the expense of Hull KR.
The stand-off converted his fourth attempt five minutes into added time to leave their hosts heartbroken after a pulsating contest at Craven Park.
Tries from Kris Welham and Vinnie Anderson saw the first half finish 6-6.
Six further tries followed as the lead changed hands three times with the game poised at 24-24 before Briers' winner.
The tense victory avenged Warrington's quarter-final defeat in 2006, when then National League One side Rovers sprung a famous victory to secure a place in the last four.
Warrington celebrate 'awesome' win
In sweltering conditions in East Hull, the home side took the lead inside three minutes when Paul Cooke's superb long pass allowed Peter Fox to send through Welham under the posts.
But Warrington were level 14 minutes later when Michael Monaghan's deft pass fed Anderson, who shrugged off the challenge of Lee Briscoe to touch down from close range, with Chris Bridge adding the extras.
Both defences stood firm in the face of numerous attacks to ensure the game was level going into the half-time interval.
And it was the visitors who took control early in the second half when Bridge released Matt King, whose right-wing burst sent through Jon Clarke.
The score incensed the home fans, who were adamant the hooker took a forward pass from his Australian team-mate before touching down under the posts.
But the Robins regained the lead with quick tries from Clint Newton and Ben Galea, the latter capitalising on a horrible mistake from Warrington full-back Richie Mathers.
Rovers extended their lead to 10 points on the hour with one of the tries of the year, brilliantly finished by Jake Webster.
Scott Murrell shaped to kick on the last tackle only for the Warrington defenders to hold back, allowing the loose forward to release Daniel Fitzhenry.
The interchange burst into Warrington's half before offloading inside to Michael Dobson, who sent the killer pass out to the New Zealander to touch down an exhilarating try.
Newton vows to deliver for Hull KR fans
But the visitors regained their composure and reduced the deficit to four points when King touched down Brier's clever crossfield kick, a score brilliantly converted by Bridge from the right touchline.
And Bridge once again put the visitors in front after he finished off a powerful burst from Adrian Morley, adding the extras with the boot.
A Dobson penalty levelled the scores just before full-time, forcing the match into a sudden-death golden-point thriller.
And after three unsuccessful drop-goal attempts, Briers finally nailed the fourth for the crucial one point - and a place in the last four.
Hull KR coach Justin Morgan: "I know players were out on their feet and to play extra-time might have been prolonging the agony. I suppose golden point is the way to go.
"It's difficult, but because it's cup rugby, you have to have a winner.
"We're disappointed. I thought the effort was great but our execution at times was poor."
Warrington coach Tony Smith: "I don't think either team will be happy with their performance.
"At half-time I thought we were pretty ordinary and Hull KR weren't as good as I've seen them in recent times.
"There were pleasing aspects but it wasn't until we went two scores behind that we started to defend with gusto."
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