The Reds were staring down the barrel of another aberration in south London when Fraizer Campbell opened the scoring for the Eagles in the 15th minute at Selhurst Park.
But Brendan Rodgers' side were able to make the most of their dominance by responding through Daniel Sturridge four minutes into the second half before Adam Lallana grabbed the eventual winner with a follow-up finish just before the hour-mark.
Potters veteran Peter Crouch allowed the visitors to go ahead in the 10th minute before Joshua King replied with the first of his treble in the 36th minute.
The former Manchester United youngster added a second in the 50th minute, after Rudy Gestede's penalty on the stroke of half-time, before completing his hat-trick in the 55th minute to send the Lancashire outfit through in fine fashion.
The Nigerian striker added to the two goals in his past two league games by hitting the back of the net in the 20th and 57th minutes while James Morrison and leading scorer Saido Berahino also tallied in the Baggies' big win.
And in the all-Championship meeting, Reading edged past Derby County 201 at the iPro Stadium thanks to second-half goals from Hal Robson-Kanu and Yakubu either side of Darren Bent's 61st-minute leveler.
Sunday and Monday's remaining fifth round fixtures are as follows:
Aston Villa (PREM) v Leicester City (PREM) - Villa Park, Birmingham Bradford City (L1) v Sunderland (PREM) - Valley Parade, BradfordArsenal (PREM) v Middlesbrough (CHA) - Emirates Stadium, London Preston North End (L2) v Manchester United (PREM) - Deepdale, Preston - *Monday night
2014/15 FA Cup - fifth round
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