Antti Niemi made a double save from Sam Parkin and Owen Garvan, though Richard Naylor eventually headed Town in front.
Darren Powell equalised, heading home a superb Wise cross, before Garvan put Town in front again from 20 yards.
Tomasz Hajto forced a good save from Lewis Price and Nigel Quashie hit the post, but the pressure told as Wise equalised with a diving header.
Southampton boss Harry Redknapp:
"I've never seen a team create and miss so many chances. If we still had Peter Crouch and Kevin Phillips up front we'd have won by seven.
"It was not a great point. In fact it was very much two points lost so far as
we are concerned.
"We should have won comfortably. We played some tremendous football and three points were for the taking."
Ipswich: Price, Wilnis (Richards 45), Naylor, De Vos, McEveley, Peters (Juan 54), Horlock, Garvan (McDonald 77), Currie, Parkin, Bowditch.
Subs Not Used: Magilton, Supple.
Booked: Garvan, Horlock.
Goals: Naylor 36, Garvan 61.
Southampton: Niemi, Hajto, Lundekvam, Powell, Higginbotham, Kosowski (Walcott 82), Oakley, Quashie, Wise, Ormerod, Fuller (Blackstock 90).
Subs Not Used: Smith, McCann, Delap.
Goals: Powell 50, Wise 69.
Ref: P Joslin (Nottinghamshire).