Pablo Counago pulled one back to set up a nervy finale but Roy Keane, who lifted the famous old trophy four times with Manchester United, will not be repeating the trick as Ipswich boss this season.
Instead Alan Pardew, a beaten finalist as a player with Crystal Palace and as manager of West Ham, takes his in-form League One side into the last 16.
Saints already have one foot in a Wembley final this season, leading MK Dons 1-0 after the away leg of their Johnstone's Paint Trophy encounter earlier in the week.
And they kept up their fine cup form with a deserved success from an entertaining tie at St Mary's.
Pardew gave an immediate debut to Lee Barnard, who only arrived from Southend 24 hours earlier, and the striker had a glorious chance to open his account after 10 minutes but his volley flew straight at Ipswich goalkeeper Arran Lee-Barrett.
At the other end Saints' former Ipswich keeper Kelvin Davis kept out efforts from Grant Leadbitter, Jonathan Walters and Damien Delaney.
But it was Saints who took the lead in the 31st minute through a screamer from Thomas.
The full-back, overlapping out on the right-hand corner of Ipswich's penalty area, met a Lee Holmes pass with a stunning half-volley which flew across Lee-Barrett and crashed into the back of the net.
Ipswich thought they had equalised just after the interval when centre-half Radhi Jaidi failed to deal with a long throw from Carlos Edwards and the ball ended up in Southampton's net, but referee Andy Hall disallowed the effort.
Ex-Saints striker Stern John then met a cross from Liam Rosenior but his header flew wide.
Southampton missed two chances in quick succession to double their lead. Lee Holmes crossed towards Adam Lallana but his effort was cleared off the line before Jaidi put a header wastefully wide.
But they did grab a second 15 minutes from the end when Lee-Barrett spilled Rickie Lambert's free-kick and Reading loanee Antonio tucked in the loose ball.
Lambert almost hit an audacious third after spying Lee-Barrett off his line but his long-range lob hit the top of the net.
Counago set up a grandstand finish when he tucked away Lee Martin's pass but Saints survived a frantic five minutes of stoppage time to secure their passage into the fifth round.
Source: Team Talk
Source: Team Talk