James Beattie unlocked this cup tie to send Saints marching into round four.
With half an hour gone he moved off his marker, Tony Butler, to chest down a long chip from Rory Delap way out on the right to sidefoot his eighth goal this season.
Until two late defensive lapses let them down, City were always matching a side nearly 50 places above them with their determination and hard running.
City manager Danny Wilson said: "It was a harsh scoreline, but we played very well and created a lot of chances.""But against Premiership opposition you have to take your chances when they come but we didn't."City almost scored first when a shot from Craig Woodman found it's way past keeper Antti Niemi, but on the way in it had touched Lee Peacock's head and City's topscorer was fractionally offside.
Niemi had a busier time in the first half than City's Steve Phillips, beating down shots from Luke Wilkshire and Peacock.
In blocking a Wilkshire drive, he strained his groin and had to be replaced in the second half by Welsh keeper Paul Jones.
For all their quality in build-up, Saints were making little impression on a home defence with three centre-backs. When they got through they found Phillips in top form and he made one magnificent save from young Frenchman Fabrice Fernandes on the eve of his 24th birthday.
But City, having given so much in attack, many raids stemming from the accurate left foot of Brian Tinnion, began to look slightly tired.
A bad mistake let Brett Ormerod in for the second goal, an accurate finish blasting between Phillip's right hand and the post.
Ormerod had reclaimed his place in attack and showed no sign of his throat infection in a lively, bustling performance.
With only minutes left he was upended by Danny Coles just outside the box and Graeme Le Saux's free-kick took a deflection off the wall.
It was the sort of luck City, as a second division side, were always denied.
Southampton's manager Gordon Strachan said: "City did very well and I have to be pleased with the result.
"Actually I'm more than happy to have won 3-0, for we have played better this season and lost."