The equaliser was Reid's ninth goal of the season and keeps Plymouth around the playoff positions in the table.
The hosts started the game brightly, with a fairly dominant display in the early stages.
Plymouth came out fighting after the break and were awarded a penalty after Reid was brought down in the area.
Reid stepped up to claim the equaliser and Plymouth held on to their parity for the remaining 20 minutes.
The result means that automatic promotion chasers Burton drop into the playoffs, with Plymouth sitting just behind the Brewers in sixth.