Paul McCallum's third-minute opener on his home debut had given the Shots an early lead but the Brewers responded just before half-time through Robbie Weir.
And despite the attentions of three home defenders, Symes got away a perfectly-placed volley from the edge of the box after 65 minutes to fire Burton to a 2-1 victory and up into second place in League Two.
The Shots made the perfect start when McCallum fired home, the West Ham loanee converting from a narrow angle on the left.
Burton appeared stunned by the early strike and both Lionel Ainsworth and McCallum were a constant danger in the first half-hour.
However, on the stroke of half-time the Brewers drew level as Weir volleyed through a crowd of bodies after Zander Diamond had headed the ball back into the danger area.
That goal gave Burton the momentum and midway through the second half Symes brought down Anthony O'Connor's ball forward before hitting a stunning left-footed volley on the turn for the winner.