Fulham had looked like ending a five-match winless streak at Craven Cottage following Steve Sidwell's first-half strike but now the run is six since the April 1 defeat of QPR.
Twice Dimitar Berbatov netted when offside before McAuley met Chris Brunt's corner with an emphatic header in the first of six minutes of stoppage time.
The Baggies had been toiling up until that point, but returned to the West Midlands content, while Martin Jol's hosts and their fans were left frustrated, a vocal minority even calling at the final whistle for the Dutchman to be relieved of his duties.
The Baggies' most recent Premier League goal had come against a Manchester United side managed by Sir Alex Ferguson.
But the prospects of ending the drought appeared promising - on paper at least - as Steve Clarke deployed a heavyweight strike pairing of Victor Anichebe and Nicolas Anelka.
Anichebe and on-loan Marseille midfielder Morgan Amalfitano made their Baggies bows, but Stephane Sessegnon, another deadline day signing, missed out due to a delay in obtaining his work permit.
Amalfitano was part of a visiting midfield which stifled Fulham's efforts in the final third until Bryan Ruiz flashed an early effort wide after Pajtim Kasami's cross was only half cleared.
Philippe Senderos was marshalling Anichebe well and the Baggies made little forward progress other than a Brunt drive which was always curling away.
As the battle for midfield supremacy continued, Fulham won the game's first corner and took the lead.
Source: PA
Source: PA