Accies winger Dougie Imrie forced the only serious save of the 90 minutes with a brilliant 30-yard free-kick and the game looked destined to finish goalless.
But Vernon slotted home a dramatic late winner which could have a major say in the relegation battle and the nature of Aberdeen's season.
Aberdeen claimed their first win in eight games when Brown took charge for the first time at Hibernian on Boxing Day and this victory secured consecutive SPL successes for the club for the first time since August.
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