In what was a scrappy opening period, Shane Long took advantage of a fortunate ricochet to give the Premier League high-flyers the lead early on.
Ipswich toiled away, but they were largely wasteful despite getting into some good positions.
David McGoldrick posed the greatest threat for the home side, but he often had to drop deep and thus was less of a direct threat.
Conditions didn’t help, but Mick McCarthy will be disappointed his side never really got going, and offered very little in the final third.
Southampton’s reward for their battling victory is a tie against Crystal Palace in the fourth round at St Mary’s.
The pitch played its part, but the football was lacking in quality right from the off, with both sides struggling to find that killer pass.
Shane Long’s workrate was causing the hosts real problems, as his endeavour presented Victor Wanyama with a chance to open the scoring, but with Ipswich goalkeeper Bartosz Bialkowski stranded, he volleyed high, wide and not so handsome.
Stephen Hunt did find the net early on, but the veteran Irishman’s effort was chalked off for offside and McCarthy’s promotion chasers struggled to make inroads in the first half.
It was Long who was in the right place at the right time to break the deadlock for the visitors.
Neat team play and a clever turn saw Ward-Prowse through on goal. Ipswich captain Luke Chambers produced a wonderful challenge to deny the England Under-21s midfielder, only for the ball to fall for Long to fire home an impressive first-time strike.
Dusan Tadic saw a goal-bound shot blocked as the first half entered stoppage time – a period in which the visitor’s key man Wanyama sustained a game-ending hamstring injury.
Things could have got even worse for Saints after their former striker McGoldrick got free, but he could only fire into the side-netting.
Long continued to prove a nuisance when play resumed after half-time, when Town at last began to offer a threat.
Substitute Tyrone Mings provided a fine cross which Darren Ambrose directed toward goal, only to see a previously untested Fraser Forster make a smart save.
Ipswich were now enjoying more possession but too often the final ball let them down, with Saints skipper Jose Fonte helping his team hold firm at the back.
As the clock wound down both sides had wayward efforts rightly jeered by both sets of fans, but it was the Saints who progressed to the next round.