Championship club Cardiff City, West Bromwich Albion and Plymouth Argyle were named as Town's home opposition.
The Second Round saw Swindon beat Wrexham in Wales a couple of weeks later, Gordon Greer scored the only goal ten minutes time.
Town were knocked out of the competition in the Third Round to Premier League outfit Fulham, Bobby Zamora scoring for the Cottagers.
Wolves manager Mick McCarthy fielded an under strength team but did enough to beat Swindon Town 6–5 in a penalty shoot-out after 120 minutes of football without a goal.
Swindon Town were drawn to play Exeter City at St James Park where a late Stuart Fleetwood strike cancelled out Anthony McNamee's goal in the first half.