Brown Ideye handed the Baggies an early lead, the £10million man’s first goal for the club, before the visitors hit back thanks to Tom Ince and Robbie Brady either side of the break.
But McAuley equalised with three minutes left on the clock and then just a minute later Berahino slotted home to rescue Alan Irvine’s men and steal it 3-2.
Both teams were completely changed from the weekend with Liam O’Neil, Sebastian Blanco and Cristian Gamboa making their full Albion debuts.
Hatem Ben Arfa started for Hull along with Paul McShane, who spent a year at the Black Country outfit before leaving for Sunderland in 2007.
Despite their changes both teams were composed early on with Brady heading over and Youssouf Mulumbu’s low effort deflected inches wide.
But Albion slowly began to take control and struck when Ideye opened his Baggies account on 15 minutes.
O’Neil’s cross was perfect for Blanco but he was denied from point blank range by Steve Harper, only for Ideye to stab in from two yards.
The Nigeria international injured himself while scoring though and was immediately replaced by Georgios Samaras.
The Greece striker chipped over after 31 minutes but Albion were in charge despite failing to add to their lead.
Hull lacked the quality or the patience to hurt the Baggies, who dominated their ragged visitors, until they turned the game inside 10 minutes.
First, Yannick Sagbo found Brady scampering down the right and he crossed for the unmarked Ince to smash in at the far post on 41 minutes.
Then, five minutes into the second half, Ben Arfa tricked his way inside and his ball split the Baggies’ defence for Brady to collect and steer into the corner from eight yards.
The Baggies had been punished and their sloppy play gave no hints of the late drama to come.
Blanco was off target with a free kick for Albion but Hull were inches away from adding to their lead when David Myler’s volley arrowed wide.
The dynamic had changed with Hull in control, the previously quiet Ben Arfa a more central figure.
And predictable Albion struggled until the death when they finally rallied.
A fine double save from Harper thwarted Claudio Yacob and Berahino before Albion levelled with three minutes left.
McAuley volleyed in from 10 yards after Hull had failed to clear a corner and Berahino won it a minute later.
Silvestre Varela slipped the ball through to Berahino and the England Under-21 international skipped past Harper to squeeze in from a tight angle and set up a trip to Bournemouth in the last 16.