Non-league Blyth Spartans, Southport and Gateshead were knocked out of the FA Cup third round on Saturday, leaving Conference side Wrexham as the lowest team left.
Northern Premier League Blyth, who play in the seventh tier, let slip a two-goal lead to lose 3-2 to Birmingham.
Wrexham visit Premier League club Stoke on Sunday.
West Brom's emphatic win came in Tony Pulis's first home game in charge following his appointment on New Year's Day.
England Under-21 striker Saido Berahino scored four goals, taking his tally for the season to 13.
League One Rochdale added more misery to Nottingham Forest boss Stuart Pearce as an early Peter Vincenti penalty condemned the Championship side to a third successive defeat and a seventh game without victory.
|Southport have not progressed beyond round three since 1966||West Brom's win was their biggest in the FA Cup since beating Aylesbury United 8-0 in 1992|
|Rochdale have reached the fourth round of the FA Cup in consecutive seasons for the first time in their history||Norwich have kept just two clean sheets in their last 23 FA Cup ties|
Rochdale's league rivals Preston also secured an upset against Championship opposition, beating Norwich 2-0 thanks to two Paul Gallagher goals.
Bradford will host Millwall in a third-round replay after the two sides drew 3-3 at The Den, while League Two Cambridge United secured their place in the fourth round by beating league rivals Luton 2-1.