Antonio had only been on the field for a minute after coming on as a sub before scoring what proved to be the winner and send Saints through to the fifth round.
Ipswich started the brighter and nearly went ahead after two minutes when Grant Leadbitter's clever free-kick from 25 yards was well saved by Saints keeper Kelvin Davis.
The early promise from the visitors failed to materialise as both teams seemed content on playing an unattractive long-ball game.
That was until the 31st minute when Saints full-back Wayne Thomas sparked the game into life with a spectacular 25-yard rocket that flew into the top corner.
Ipswich had the ball in the net five minutes into the second half direct from a Carlos Edwards throw-in.
It was quickly ruled out by the referee who adjudged the ball not to have been touched on its way past Davis.
Southampton should have doubled their lead just past the hour mark when a dangerous Barnard cross picked out Radhi Jaidi at the back post, but the former Bolton man somehow headed over from two yards.
The Tractor Boys looked out of ideas going forward and struggled to create any clear-cut chances against a resilient Saints defence.
The game was put beyond doubt 20 minutes from time when Rickie Lambert's fierce free-kick from 20 yards was parried straight to the on-rushing Antonio, who duly slotted in his second goal of the week after only being on the field for a minute.
Pablo Counago pulled a goal back in the last minute with a neat finish past Davis, but it proved to be a mere consolation for Roy Keane's Championship side.