This season, more than any other, an extended cup run was essential for the Lions.
Former loan striker Kevin Davies' last minute equaliser at St Mary's ten days earlier had ensured a lucrative replay at the New Den in front of the TV cameras, but Millwall's recent upsurge in form encouraged them to want more.
The exit of a significant portion of Premiership sides before the fifth round stage ensured Southampton's participation was more than a mere distraction from a fight for a European place.
The Saints, lucky to still be in with a second chance, pushed that fortune further in only the third minute as Charlie Hearn charged down Francis Benali's clearance, but the full back atoned as he chased down and blocked the youngster's shot.
From then on the visitors gradually took control despite Millwall's 4-5-1 formation that was intended to deny them space.
Captain fantastic Chris Marsden seemed to be everywhere and midfield partner Oakley opened the scoring with a crisp half-volley in the 22nd minute.
Even at that stage a route back into the game appeared unlikely for Mark McGhee's men. But in a moment of magic, Paul Ifill's flick released Steve Claridge and the striker's cross was turned in at the second attempt by Steven Reid.
To their credit Millwall gave as good as they got after the restart and Antti Niemi did well to tip over Claridge's shot.
At the other end Tony Warner held Anders Svensson's drive and England prospect James Beattie sent a header against the post.
In a frantic finale Ifill and Claridge saw chances go begging, but as the game went into extra-time fatigue became a factor for the home side.
The Saints' lack of quality up front on the night did not matter in the end as Oakley snatched the all-important winner in the 102nd minute with another crisp drive to set up a home clash with Norwich City in the next round.