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After weathering a first-half storm, Derby stunned Albion by taking a 49th minute lead through Chris Porter.
But a three-goal Albion blitz in the space of 15 minutes turned the game on its head.
Brunt's eighth goal of the season in the 67th minute drew Albion level and he completed the comeback ten minutes later. Substitute Simon Cox, who set up Brunt's opener, then sealed the victory eight minutes from time,
After collecting just a point from the previous two games, a win was vital for Albion and it also lifted them back into second place following Nottingham Forest's defeat at Leicester City.
Derby, who have now lost their last two games, looked set to pull off an impressive win after Porter's second goal of the season, but were swept aside by the storming Albion fightback.
Albion made their predictably dominant start but they could not find a way through a determined Derby rearguard.
Jerome Thomas and Brunt both went close before Robert Koren saw his drive deflected wide.
Koren then blazed over the bar before a desperate late block by Derby captain Robbie Savage kept County on level terms.
Thomas picked out Luke Moore and he looked set to score at the far post in the 31st minute.
But Savage slid in to deflect Moore's shot to safety - with Albion's claims that he stopped the ball with his hands being ignored by referee Phil Crossley.
Derby only came to life as an attacking force in the closing stages of the half when Jake Buxton fired wide, before Michael Tonge was inches away from converting a Stephen Pearson cross.
Albion then had further penalty appeals rejected when Thomas went down under challenge from Paul Green, but again Crossley waved away their protests.
While Albion had started the first half positively, it was Derby who were quicker out of the blocks after half-time and were rewarded when Porter pounced.
Albion's defence was completely undone by a chip into the area by Savage and when the ball found its way to Porter he made no mistake at the far post.
Derby should quickly have doubled their advantage only for on-loan Arsenal forward Gilles Sunu to lift the ball over the bar from close range.
That was costly as Albion took full advantage of their let-off when Cox picked out Brunt on the edge of the area and he beat Stephen Bywater from the edge of the area.
Brunt then put Albion in control by bundling home a corner from Graham Dorrans.
Derby then tried to chase the game and were caught out at the back by Cox, who converted a through ball from fellow substitute James Morrison.