Southport looked set to earn a replay against Championship high-flyers Derby but Chris Martin's injury-time penalty gave the Rams a 1-0 win.
Two Championship sides were knocked out by League One opponents.
Nottingham Forest's miserable run continued as Peter Vincenti's 12th-minute penalty earned Rochdale a 1-0 victory at Spotland.
Paul Gallagher was the hero for Preston as his second-half goals earned them a 2-0 win over Norwich.
It looked like Millwall would go the same way against Bradford at The Den but Ricardo Fuller's second of the game in the 83rd minute made it 3-3 to earn a replay.
Having led through Billy Knott's early goal, visitors Bradford found themselves behind when Scott McDonald and Ricardo Fuller scored for Millwall.
But a Sid Nelson own goal drew Bradford level four minutes later and Knott thought he had provided the winner in the 76th minute, only for Fuller to have the final say.
Tony Pulis' debut as West Brom manager could scarcely have gone better as he watched his side defeat Conference side Gateshead 7-0.
Saido Berahino scored a hat-trick in 11 minutes either side of half-time and added a fourth in injury time, with Victor Anichebe, Chris Brunt and James Morrison also on the scoresheet.
Swansea were also among the goals at Tranmere as they ran out 6-2 winners.
Nathan Dyer's 34th-minute goal was all that separated the teams at half-time but Tom Carroll and Modou Barrow, with his first Swansea goal, extended that to 3-0.
Max Power pulled one back, and Cole Stockton reduced the deficit to two again after Bafetimbi Gomis had scored, but Wayne Routledge and Gomis added late goals.
In the day's only all-Premier League tie, Leicester continued their encouraging form as Leonardo Ulloa's 39th-minute goal gave them a 1-0 win over managerless Newcastle.
Wigan are struggling badly in the Championship and could find no solace in the FA Cup.
The Latics won the trophy in 2013 and reached the semi-finals last season but went down 1-0 to local rivals Bolton thanks to Zach Clough's goal 14 minutes from time.
Chris Hughton's debut as Brighton manager was a happy one with very late goals from Lewis Dunk and Chris O'Grady earning a 2-0 win at Brentford.
Championship leaders Bournemouth trailed Rotherham early on after Richard Brindley struck in the 10th minute but roared back to win 5-1 with goals from Shaun MacDonald, Junior Stanislas, Ryan Fraser and two from Yann Kermorgant.
Cambridge won the all-League Two tie against Luton 2-1.
Robbie Simpson put away the rebound after his penalty was saved before Ryan Donaldson made it 2-0, and Michael Harriman's 74th-minute goal turned out to be a consolation.
Nick Blackman's goal led Reading to a 1-0 win at Huddersfield, while the matches between Doncaster and Bristol City and Fulham and Wolves will be decided by replays.
The latter was goalless, while at the Keepmoat Stadium Matt Smith cancelled out Luke McCullough's opener to earn City a 1-1 draw.
The start of Barnsley's clash with Middlesbrough was delayed by fears over a gas leak, and it was the visitors who emerged triumphant 2-0 thanks to goals from Jelle Vossen and Daniel Ayala despite having Adam Clayton sent off.
A first-half floodlight failure at Charlton delayed matters against Blackburn, who eventually ran out 2-1 winners.
Chris Taylor put Rovers ahead in the fourth minute and scored the winner in the 59th minute after Charlton, who also had Yoni Buyens sent off, had levelled through Johann Berg Gudmundsson.