Darren Ambrose fired the Championship side ahead after 19 minutes but they were unable to hold onto the lead.
Morgan Schneiderlin levelled things for the hosts with an opportunistic finish three minutes after the half hour.
The Premier League side dominated the final hour of play but were unable to find a way through a resolute Ipswich defence, with goalkeeper Dean Gerken making a string of impressive saves.
Graziano Pelle and Shane Long were both guilty of wasting chances in the Town penalty area, while Mick McCarthy's team soaked up waves of pressure.
They were able to hang on, meaning the sides will meet again at Portman Road to contest a place in the fourth-round.
With Ronald Koeman keen to progress in the competition, Long and Schneiderlin were the only two Southampton players to come in after their Premier League victory over Arsenal on New Year's Day.
But it was the visitors - who made six changes - that started brightest, creating the opening chance after 14 minutes as Stephen Hunt combined well with David McGoldrick, only for Fraser Forster to pull-off a good save.
Ipswich continued to threaten and they got their reward in the 19th minute as Ambrose placed a looping header out of Forster's reach - the midfielder converting former Southampton academy player Tyrone Mings' left-wing cross.
The goal appeared to wake Southampton up and within the space of 60 seconds midway through the half Pelle and Steven Davis went close, the latter denied by Gerken's legs.
Ipswich's goalkeeper was proving a tough man to beat as he denied James Ward-Prowse but there was nothing he could do after 33 minutes as Schneiderlin capped his 250th Southampton appearance with the equalising goal.
A mix-up between Gerkan and Christophe Berra allowed the midfielder to nip in between them and flick the ball into the net from 10 yards.
Southampton finished the half in the ascendancy and they continued to control proceedings in the early exchanges after the break, but Pelle and Long both wasted good chances.
Gerkan was back to his old tricks after an hour as another Southampton move saw Davis find Pelle, but the Italian's effort was well stopped.
Koeman's decision to introduce Lloyd Isgrove gave the hosts an injection of pace, but it was Long who thought he had won the game after 72 minutes, only for his effort to be ruled out by Martin Atkinson.
Long had a late chance to be the Southampton hero but the Irishman's control let him down and Ipswich clung on for a replay.
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