The decisive moment, at the Merseyrail Community Stadium, arrived on the brink of half-time when the visitors had Luke Howell sent off for violent conduct.
And the struggling League Two side were made to pay early in the second half as John Marsden and Danny Hattersley fired Southport into a two-goal lead.
Marsden opened the scoring on 50 before Hattersley added a second from the penalty spot after the striker had been fouled by Matt Partridge who was shown a yellow card for his misdemeanour.
League One Doncaster made light work of Weston-super-Mare at the Woodspring Stadium where Curtis Main, Theo Robinson and James Coppinger were on target before the break, with the Yorkshire visitors going on to win 4-1.
Main opened the scoring with a low 12-yard strike on 16, with Robinson doubling the margin from close range 19 minutes later to leave the Conference South hosts with a mountain to climb.
And to make matters even worse, the prolific Coppinger (45) added a third after latching on to a pass from Richie Wellens who made it 4-0 on 63. Liam Monelle snatched a consolation goal in the final minute.
Ryan Flynn netted twice for Sheffield United who eased past fellow League One side Crewe 2-0 at Bramall Lane.
Flynn???s first came on 19, touching home from close range, before sealing the deal 13 minutes from time.
At the Cherry Red Records Stadium in south London, hosts AFC??Wimbledon recovered from an early setback to beat York 3-1.
Wes Fletcher had given the northerners a fifth minute lead with an excellent rising shot from 30 yards, which was the way it remained until 18 minutes from time when Jack Smith equalised following Adebayo Akinfenwa???s assist.
Matt Tubbs broke York hearts with a brace of goals in the final nine minutes to secure a trip to Wycombe Wanderers in round two.
In the only match that was not a first round replay, Essex non-leaguers Concord Rangers drew 1-1 with Mansfield at Field Mill where both goals arrived during the opening 20 minutes.
After Danny Glozier had put through his own net to give the hosts the lead, Jordan Chiedozie levelled matters 60 seconds later.
Chiedozie, son of former Spurs player John, found the top left-hand corner of the net from 20 yards. Cambridge United await in the second round for whoever wins the replay.
At Telford, first half goals from Andrew Parry and Tony Gray fired the hosts into a two-goal lead against Basingstoke who eventually lost 2-1 in the battle of the non-leaguers.
Louie Soares pulled a goal back in the 52nd minute before both sides were reduced to 10 men. Telford lost Mike Grogan to a second bookable offence on 57, with Jamie Brown receiving his second yellow card in the final minute.
Rochdale scored twice in the final seven minutes to see off Northampton 2-1 with Oliver Lancashire heading the winner in the fourth minute of injury time. The visitors had taken the lead as early as the fourth minute through Ivan Toney.
Accrington Stanley also recovered from a goal down to beat Notts County by the same 2-1 scoreline while Liam Lawrence???s 53rd minute goal sealed a 1-0 victory for Shrewsbury over Walsall who had Adam Chambers dismissed for a bad foul seven minutes from time.
FA Cup Second Round draw:
Oxford United v Tranmere Rovers
Bury v Luton Town
Wrexham v Stevenage or Maidstone
Scunthorpe United v Worcester City
Colchester United v Peterborough United
Wycombe Wanderers v Wimbledon
Accrington Stanley v Yeovil Town
Hartlepool United v Blyth Spartans
MK Dons v Chesterfield
Southport v Eastleigh
Gateshead v Warrington Town
Oldham Athletic v Doncaster Rovers
Preston North End v Shrewsbury
Barnsley v Chester
Bradford City v Dartford
Sheffield United v Plymouth Argyle
Cheltenham Town v Dover Athletic
Cambridge United v Mansfield Town or Concord Rangers
Bristol City v Telford
Portsmouth or Aldershot v Rochdale
Ties will be played on December 5, 6 or 7.