Warrington came back strongly after they had trailed 22-10 to lead by two points with minutes remaining but a Dobson penalty levelled the game, only for Briers to land a sudden-death drop goal with his fourth attempt, five minutes into extra time.
Golden point was the only way that the sides could be separated, with the first half ending dead-locked at 6-6 and the second 40 closing with the scores tied at 24-24, both teams scoring four tries and kicking four goals.
Warrington began to find their feet in the sunshine and their pressure eventually told when Clarke passed left from the play-the-ball to Monaghan, who put Vinnie Anderson in to score with a clever inside ball to level the match.
Both sides had chances in the remainder of the half, which was played at a frenetic pace in energy sapping heat, but neither could find a way through some desperate scrambling defence.
Warrington emulated Hull KR’s flying start in the second-half with Clarke scoring after three minutes for the Wolves when the ball was spread wide inside their own half to King, who raced down the wing before passing back inside to Clarke for the finish.
Full back, Mathers, was left helpless by a horrible bounce leaving the onrushing Ben Galea to touch the ball down and the game looked all but over when Rovers’ Jake Webster finished off a breathtaking move, started by quick thinking from Murrell who sped into space after originally shaping to kick.
Warrington would not roll over, however, and Matt King brought them back into contention, keeping his composure to finish instinctively from Brier’s chip wide, judging the inside bounce to perfection.
Minutes later they were in front when Morley strode powerfully through the middle, the ball finding Briers and then Bridge who touched down and then kicked Warrington into a two point lead.
Dobson coolly levelled the scores with two minutes to go after the Wolves were caught offside and extra time looked a certainty until Rovers’ Walker dropped the ball near his own line.
Briers wasted the glaring drop-goal opportunity to win the game in normal time but, after he had missed two more from distance and Paul Cooke’s attempt had been charged down in extra-time, he held his nerve to fire over the winner, sparking wild celebrations from the Warrington supporters and players.