In a dramatic sudden death finale, the Wolves stand-off nailed the winning drop goal after he had failed with no fewer than four earlier attempts as the game went to Golden Point after a 24-24 tie.
Hull KR stand-off Paul Cooke also failed with a drop-goal attempt in one of most dramatic finishes in Challenge Cup history.
Between Briers and Chris Bridge they rallied Warrington, who had trailed 22-12 with just under 20 minutes to go.
Wolves finished the stronger side to maintain their revival under England coach Tony Smith and looked to have won the tie in normal time after scoring two tries in five minutes to edge 24-22 ahead.
Michael Dobson then tied the scores for a third time with a 78th-minute penalty to set up the dramatic finish.
But Briers perservered and ended KR's six-game unbeaten run to scupper the Humberside outfit's dreams of walking out at Wembley.
It started well for KR caught the Wolves cold with a try after only three minutes. A long pass by Cooke released winger Peter Fox and centre Kris Welham went over.
But Rovers did not build on their flying start and, after conceding two goal-line drop-outs, they cracked on 16 minutes.
Wolves' loose forward Vinnie Anderson took Michael Monaghan's pass to crash over by the posts and Chris Bridge's goal levelled the scores.
It stayed at 6-6 until half-time, then Wolves went in front three minutes into the second half when Simon Grix got Matt King charging down the wing and the supporting Jon Clarke was inside to finish off.
But Rovers struck back with two tries in five minutes to regain the lead. Front rower Clint Newton took Dobson's short pass to stride over, then second rower Ben Galea pounced on Cooke's kick.
Dobson maintained his accuracy to kick Rovers into an 18-12 lead. And KR looked to have clinched the win with a glorious 50-metre try on the hour.
Loose forward Scott Murrell shaped to kick on the last tackle only for Wolves to hold back and he released Daniel Fitzhenry.
He juggled with the ball before finding Dobson and his long pass sent Webster racing over to make it 22-12. That signalled the fightback as King gathered Briers' kick to the corner to touch down.
And it was all square on 70 minutes later when hooker Mickey Higham got Adrian Morley into a gap and he and Briers got Chris Bridge over.
Bridge converted only for Dobson to level at 24-24, setting the stage for Briers.
SCORERS - Hull KR: Tries: Welham, Newton, Galea, Webster. Goals: Dobson 3. Warrington: Tries: Anderson, Clarke, King, Bridge. Goals: Bridge 4. Drop Goal: Briers.
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