The home side took a 32nd-minute lead when Kirsty Bell turned the ball in via a corner kick, following up a save by Robyn Levett.
It was 2-0 early in the second half, Laura Gilbank’s cross beating all and ending up in the back of the net.
Swindon were given the chance to halve the arrears on 8 minutes but the spot-kick was fired over the bar, highlighting their inaccuracy in front of goal on the day.
Southampton Women, who have won all their games in the regional league, now travel to more FAWPL opposition in South East Division 1 side Cambridge United after the new year.
Sunday 8 January 2017
SSE WOMEN’S FA CUP 2ND ROUND – REVISED DRAW
Long Eaton United v Brighouse Town
Derby County v Sheffield United
West Bromwich Albion v Radcliffe Olympic
Nottingham Forest v Wolverhampton Wanderers
Middlesbrough v Leicester City Women
Blackburn Rovers v Hull City
Liverpool Marshall Feds v Newcastle United
Coventry United v Milton Keynes Dons
C&K Basildon v Keynsham Town
Lewes v Cardiff City
Tottenham Hotspur v Gillingham
Plymouth Argyle v AFC Wimbledon
Cambridge United v Southampton Women
Charlton Athletic v Portsmouth