Albion are through to the FA Cup quarter final for only the fifth time in their history thanks to an 117th minute extra-time winner from Danny Welbeck.
Alexander Isak put Newcastle in front from the penalty spot in the first half – but Yankuba Minteh equalised for Albion against his old club.
Tariq Lamptey for Albion and Anthony Gordon for Newcastle were sent off.
The match was at times like a basketball match and thoroughly end to end.
Joe Willock missed a glaring chance for Newcastle in the second half and right at the death two minutes into injury time Fabian Schar looked to have given Newcastle the win.
However, this was eventually ruled out by VAR.
Albion’s late late winner came courtesy of a Solly March assist and a spectacular outside of the boot flick from Welbeck.