Despite trailing by ten points at one stage, the Robins showed terrific spirit to hold their nerve and ultimately emerged as worthy winners with winger Byron Ford claiming a hat-trick.
Warrington looked set to pull clear in the opening stages as Logan Swann helped himself to two early tries.
First he turned and wriggled his way over from close range, then bulldozed through a tackle out wide to touch down.
With Chris Bridge adding the extras the Super League outfit looked in control, but Rovers then showed just why they have won every game in National League One this season with a superb fight-back.
Full-back Ben Cockayne surged over after a clever inside pass from James Webster and moments later Papa New Guinea forward Makali Aizue touched down after the ball had rebounded kindly off the post.
Warrington seemed to have regained control when Bridge fed Stuart Reardon to score and an error from Hull's Darren Price was punished as Jon Clarke burst clear before offloading for Martin Gleeson to cross next to the posts.
But the hosts once again refused to lie down and Jon Goddard quickly replied to restore hope.
Ford then gave the Robins a real shot in arm as he took advantage of a fortunate ricochet to kick on and touch down and Morton's fine conversion from out wide ensured they went in 24-22 to the good at the interval.
The unrelenting pace continued after the break as Morton claimed a try of his own after racing on to Ben Fisher's clever kick to edge Hull six points clear.
The wire needed a quick response and got one through Henry Fa'afili as he rose superbly to collect a high kick and acrobatically ground the ball out wide, but Rovers responded in kind as Ford scored an almost identical try shortly afterwards for his second of the afternoon.
The home crowd were then in raptures as he completed his hat-trick, stretching to make it home in the corner as the covering Warrington defence failed to stop him.
However, Morton's poor goal-kicking ensured the lead stayed at just 14 and Warrington soon served notice they were not done.
Fa'afili finished well out wide to reduce the arrears and Australian Michael Sullivan then produced a fine pick-up and finish which, combined with the extras from Bridge, brought the Wolves to within four.
However, that was as close as they got and the hosts held on for a memorable victory and now take their place in the semi-final draw.
Digg
Delicious
Facebook
Reddit
Stumbleupon