Substitute Will Buckley netted with ten minutes remaining to earn Albion a share of the spoils at a rain-sodden Amex.
Such is the topsy-turvy nature of the Championship, Ipswich - starting the game in the bottom three and with just one league win to their name - looked to be heading for all three points until Buckley saved the day.
On reflection, the point was deserved but it is the visitors who will go home the most frustrated, having seen a chance to break out of the drop zone slip through their fingers.
With Albion keen to make amends for Saturday's defeat against Birmingham and Ipswich desperate for the points to kick-start their season, the first half was an open affair with chances created by both sides.
Indeed, Gus Poyet's men could have gone ahead as early as the first minute when a ball across the edge of the box by Ashley Barnes was superbly dummied by strike partner Stephen Dobbie, but Kazenga LuaLua scuffed his effort into the ground.
Albion created another chance on ten minutes when a delightful sweeping move saw Barnes receive the ball following a probing run by Andrea Orlandi. Again he looked for Dobbie, whose shot was well held by Scott Loach.
The chances kept coming and on 19 minutes Orlandi saw his dipping free-kick from the right flank tipped away for a corner by Loach, while Inigo Calderon had an effort blocked from 18 yards out.
Ipswich still looked dangerous on the break and hearts were in mouths when a cross by Andy Drury was headed across the face of goal by Michael Chopra.
Adam El-Abd also hacked an effort clear but the visitors were all smiles on 27 minutes when a deep Carlos Edwards cross from the right was headed home at the far post by Daryl Murphy.
The goal knocked the wind out of Albion's sails for a while, as they failed to get their passing game going - the best effort coming shortly before the break when Wayne Bridge played a neat one-two with Dobbie only to see his right-foot effort deflected wide.
The second half was just seconds old when Murphy again ghosted in at the far post but this time Tomasz Kuszczak was equal to the effort.
Dobbie saw a 20-yard effort deflect agonisingly wide of Loach's right-hand upright while the Town keeper also kept out a thunderous LuaLua drive.
Barnes also went close with a low effort but the visitors' rearguard stood strong as Poyet brought on Gary Dicker and Buckley in place of Dean Hammond and LuaLua - the duo helping to increase the tempo.
Dobbie had claims for a penalty turned down while Jay Emmanuel-Thomas let fly from distance in a rare break forward for the visitors.
David Lopez replaced Orlandi as a final throw of the dice and Albion got themselves out of jail when Calderon broke into the box before dinking the ball across the face of goal for Buckley to bundle home - his second goal of the season.
Ipswich sub Jason Scotland brought a save out of Kuszczak late on and although there were five minutes of injury time called by referee Fred Graham, Albion could not find the winner.
Albion: (4-3-3) Kuszczak; Calderon, Greer, El-Abd, Bridge; Bridcutt, Hammond (Dicker 63), Orlandi (David 77); LuaLua (Buckley 63), Barnes, Dobbie. Subs not used: Ankergren (GK), Dunk, Painter, Harley.
Ipswich Town: (4-5-1) Loach; Edwards, Chambers, Higginbotham, Cresswell; Emmanuel-Thomas (Carson 84), Drury, Martin, N'Daw, Chopra (Scotland 64); Murphy. Subs not used: Lee-Barrett (GK), Luongo, Ellington, Smith, Ainsley.
Referee: Fred Graham
Attendance: 24,736 (753 Ipswich Town)
Yellow cards: Hammond, Bridcutt, El-Abd (Albion)