Chris Zebroski's header had put the hosts on the front foot but John Mousinho's second-half strike prevented County from claiming their first win of the new League Two campaign.
The Exiles went ahead on 37 minutes through Zebroski.
The Welsh side's first-half pressure told when the powerful striker rose highest to nod Ryan Jackson's long throw goalwards. Brewers captain Ian Sharps had scrambled back to his goal-line but he could only force his clearance into the top corner.
Lee Minshull led the charge for a second goal before half-time when he controlled the ball with his chest and smashed a right-footed half-volley onto Jon McLaughlin's crossbar.
But Burton have enjoyed an excellent start to the season and drew level after 52 minutes.
Phil Edwards' cross from the right wing found Mousinho in space and the midfielder lashed a left-footed shot across Lenny Pidgeley and into the bottom corner.