The Addicks responded in style, though, as Ben Purrington equalised 10 minutes before half time and Bauer snatched a dramatic victory with near enough the final kick of the match.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
Charlton finished the regular season in good form to claim third place, before edging out Doncaster Rovers on penalties in the semi-finals, while their opponents stuttered somewhat ahead of their two-legged win over Portsmouth.
The side finishing fifth in League One - Sunderland this season - has not gained promotion via the playoffs since Barnsley in 2005-06, meanwhile, and only Newcastle United (eight) are on a longer winless run in matches played at the old and new Wembley than the Black Cats (six).
STARTING XI: Phillips; Bielik, Bauer, Sarr; Dijksteel, Cullen, Pratley, Aribo, Purrington; Parker, Taylor
SUBS: Maxwell, Pearce, Forster-Caskey, Reeves, Solly, Williams, Lapslie
STARTING XI: McLaughlin; O'Nien, Ozturk, Flanagan, Oviedo; Power, Cattermole, Leadbitter; Honeyman, Wyke, Maguire
SUBS: Stryjek, Matthews, Gooch, McGeady, Morgan, Grigg, Dunne
A good save from Phillips down to his left to keep out Grant Leadbitter acted as a turning point in many ways, though, as Athletic grew into the match and found an equaliser during their spell on top.
Bowyer will be the happier of the two managers at the interval after seeing his side respond well to their early setback. Here is a reminder of both teams' benches...
CHARLTON SUBS: Maxwell, Pearce, Forster-Caskey, Reeves, Solly, Williams, Lapslie
SUNDERLAND SUBS: Stryjek, Matthews, Gooch, McGeady, Grigg, Dunne
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This game looked destined to go the distance, with neither time doing anywhere near enough to claim the victory in normal time up until the moment Bauer pounced 94 minutes in to score a truly massive goal.
Charlton are heading to the Championship after a three-year absence!
We will see you again at the same time tomorrow for updates from the Championship playoff final between Derby County and Aston Villa. See you then!