Paterson struck from close range in the fourth minute of added time - just when it seemed the visitors would go home with a deserved point.
He was on hand to nudge the ball home after defender Ian Sharps got his head to a Damien McCrory corner.
Burton made the early running and Jacques Maghoma twice tested Jake Cole with low shots either side of Robbie Weir blazing over a difficult volley from 12 yards.
Cole was the busier of the two goalkeepers and had to make unorthodox use of his legs when an Alex MacDonald corner threatened to sneak inside his near post.
Plymouth came to life after the break and Jason Banton went close with an angled low shot.
Joe Bryan then had an effort pushed away by Dean Lyness for a corner which Branston headed on to the roof of the net.
MacDonald wasted Burton's best opening in the 61st minute when he fired wide at the far post.
Michael Symes then thought he had given the hosts the lead in the 76th minute but his header was disallowed for pushing, before Paterson settled matters with virtually the last kick of the game.