Albion's narrow one-goal advantage from the semi-final first leg proved to be critical as the visitors were forced to endure a nervy 90 minutes game as they surrendered their 1-0 lead on the day.
Marcus Holness looked to have settled any early Burton nerves when he glanced home a header after 21 minutes.
Gary Rowett's side went in behind at the break, however, thanks to goals from Ryan Leonard and Anthony Straker.
But Adam McGurk scored the crucial goal to book Burton a final date with Fleetwood Town as they banished the memories of last season's play-off semi-final loss to Bradford City.
Holness got Rowett's men off to a strong start when he applied a headed finish to Chris Hussey's inswinging delivery.
Leonard then produced an impressive acrobatic effort inside the area to level matters just after the half-hour mark before Straker produced another header to level the scores on aggregate.
While that gave Phil Brown and his Southend side hope, McGurk's smart finish inside the area 21 minutes from time fired Burton to the play-off final and to within one game of reaching the third tier of English football for the first time.
