The hosts had streaked into a 10-0 interval lead but two tries from Matty Ashton hauled Sam Burgess's men back into the game, before their Australian fullback Matt Dufty had a potentially match-winning effort ruled out via video replay with a minute left on the clock.
The final whistle sparked uproarious celebrations in the old stadium, and means Willie Peters' side will go to Old Trafford next Sunday standing just 80 minutes away from their first league title since 1985.
Having dominated the first half with two tries from James Batchelor and Matt Parcell, the hosts were forced to do it the hard way as Warrington came within inches of repeating their epic fightback from 12 points down to sink St Helens in a stunning quarter-final last weekend.
Ultimately, it was the visitors whose 69-year search for the domestic game's ultimate honour goes on, and they were partly let down by a sluggish first period in which it was the home side who piled on the pressure from the off.
It took 16 minutes for Rovers to break the deadlock when ex-Penrith Panther Tyrone May capitalised on a penalty by spreading the ball to the right where Batchelor piled over for the opener.
Warrington briefly thought they had levelled on the half-hour mark when Man of Steel nominee Dufty scooted through only to be pulled back for an obstruction in the build-up.
Rovers continued to hold the upper hand while Wire threatened only in fits and starts. Captain George Williams misjudged a couple of kicks and Burgess's side would have been relieved had they managed to reach the half-time break just four points adrift.
Instead Rovers hauled themselves to double figures when Joe Burgess barged over from dummy half five minutes before the interval, his try confirmed after extensive video replays and setting up Mikey Lewis to kick from the left and take Rovers into double figures.
Fresh from their comeback to beat Saints, Wire were undaunted and delivered the perfect riposte six minutes into the second period, when Toby King's persistence down the left flank teed up Ashton to stretch over from dummy half.
Josh Thewlis, however, saw a sitter of a kick drift left of the posts, and an enthralling game continued to swing from end to end.
On the hour mark, Ashton all but completed the visitors' revival by streaking over in the left corner, with only a second miss by Thewlis, admittedly from a fiendishly difficult position on the left touchline, keeping Rovers' lead intact at 10-8.
Rovers rode their luck when Ryan Hall's spill sent Thewlis within inches, and the agony continued into the dying moments as the visitors pressed desperately forward and ex-St George Illawarra and Canterbury player Dufty briefly thought he might have won it, only for the video referee to think otherwise, and the home celebrations could commence.
20°C