Blackburn were already trailing when Cole was shown a red card by referee Steve Bennett in the 63rd minute for aiming a punch at Southampton's Swedish defender Michael Svensson.
Bennett consulted his assistant before sending Cole from the field and from then on Blackburn, who had deployed him as their sole striker, were a beaten side.
Already a goal down to a free-kick from one of their former players, James Beattie, they surrendered a second with three minutes remaining to French substitute Leandre Griffit, who was making his debut.
After a dull and lifeless first half, the match sprang into life in the 59th minute when Blackburn defender Andy Todd was pulled up for a seemingly innocuous challenge on Beattie just outside the area.
Beattie smashed home the free-kick for his seventh of the season and ended a run of 457 minutes since Southampton last got on the scoresheet.
Cole was dismissed four minutes later in an incident which appeared to start when Svensson's fellow Swede and namesake, Anders, was felled, but in truth Blackburn could not use his red card as an excuse for a poor display.
The nearest they came to scoring was in the 47th minute when a free-kick from Barry Ferguson was saved by goalkeeper Antti Niemi diving to his right and the same fate befell a free-kick from Steven Reid in the 80th minute.
Gordon Strachan sent on French teenager Griffit in place of Jo Tessem with nine minutes remaining and the teenage signing from Amiens responded to rave reviews in the junior sides by taking a pass from Beattie in the 87th minute to bend a right-foot shot past the stranded Brad Friedel.
Southampton: Niemi, Dodd, Lundekvam, Michael Svensson, Le Saux, Telfer, Delap, Anders Svensson, McCann, Beattie (Marsden 90), Tessem (Griffit 82). Subs Not Used: Jones, Fernandes, Higginbotham.
Blackburn: Friedel, Reid, Gresko (Jansen 68), Martin Taylor, Todd, Flitcroft, Ferguson, Tugay, Emerton (Gallagher 68), Thompson (Neill 72), Cole. Subs Not Used: Yelldell, Johansson.
Attendance: 31,620
Referee: S Bennett (Kent).