Taylor Harwood-Bellis' own goal after four minutes gave the Tractor Boys an early advantage but Jay Robinson salvaged a point for the visitors.
In a frantic second half, Sam Szmodics hit the post for the home side while Robinson was denied a second by Ipswich goalkeeper Alex Palmer as neither side were able to grab a winner.
Southampton move onto four points, while pre-season title favourites Ipswich are yet to win after also drawing 1-1 at Birmingham on the opening night of the campaign.
Ipswich took the lead when George Hirst intercepted a wayward pass and crossed from the right for Jack Clarke to head towards goal, with the ball deflecting off Saints centre-back Harwood-Bellis' chest and into the net.
Southampton responded on the half-hour mark when former Ipswich loanee Ryan Fraser crossed for teenager Robinson to head in.
Oli McBurnie's stoppage-time goal gave Sergej Jakirovic his first win as Hull manager with a thrilling 3-2 victory over Oxford.