That proved to be costly as Ipswich came more into the game after the break, and the hosts claimed all three points through Simon Walton's penalty and Billy Clarke's first League goal, leaving Saints to rue their rotten luck, having hit the woodwork three times.
They also had an effort cleared off the line in the dying seconds when ref Mark Halsey appeared to be set to signal a goal, but decided against it, despite being besieged by visiting players.
Southampton made a confident start and went ahead in the third minute. Nathan Dyer easily beat Dan Harding and crossed for Grzegorz Rasiak to head back to Jones, who neatly turned to slot home.
John Viafara clipped the angle of post and bar with a 30-yard screamer and Rasiak's lob came back off the post, possibly with the aid of a Lewis Price finger-tip - all in the opening 12 minutes.
Inigo Idiakez, on his debut, had an inswinging corner headed off the line by Gavin Williams and Jones headed over from a Rudi Skacel corner as Saints continued to dominate.
Ipswich finally threatened on 19 minutes - loan forward Jon Macken laying the ball off to strike partner Alan Lee, whose angled shot was tipped away by former Blue Kelvin Davis.
Rasiak had the ball in the net on 34 minutes, heading home from close-range as Skacel pulled a cross-cum-shot across goal, but he was flagged offside.
Skacel shot across goal after being fed by Jones and then Davis dived to save a 25-yard effort from Williams after he surged 50 yards after receiving a quick free-kick.
Mark Noble curled a 20-yard free-kick wide from the edge of the area before Dyer was a shade lucky to stay on after a very high challenge on Harding, but received only a yellow card.
Saints had a great chance on 53 minutes when a ball over the top saw Jones beat the offside trap, but he delayed his shot and Richard Naylor got back to block, when the striker may have been better passing to one of two unmarked colleagues.
Price saved a Jones header on his far post from a Rasiak cross before Ipswich introduced new signing Sylvain Legwinski for Matt Richards and Billy Clarke for Macken.
Town were level on 67 minutes when Pedro Pele was adjudged to have caught Lee and Walton's sidefooted penalty had enough pace to beat Davis, even through he correctly dived to his left.
Dyer volleyed over from the edge of the box as Saints looked for a quick reply before Viafara and Noble were booked after a flare-up, on a day when each side had four yellow cards.
Lee missed a great chance on 73 minutes, glancing an inswinging Noble free-kick narrowly wide from just four yards.
Town went ahead on 78 minutes when sub Andrew Surman was booked for bodychecking Harding moments after coming on. Noble swung in the free-kick to the far post, Davis came but got nowhere near it and Clarke nodded home.
Saints threw everything forward from then on, and quite how Ipswich survived the bombardment is hard to say.
Sub Bradley Wright-Phillips curled his shot against the post before a sensational double-save from Lewis Price preserved Ipswich's lead.
Southampton immediately regained possession and Viafara let fly with a 20-yard volley which was heading for the top corner, only for Price to make an incredible tip-over save, as Town somehow held on.