Before kick-off, a win could have taken Roy Keane's men out of the bottom three, but other results elsewhere and this fifth draw in their last six outings left Town four points from safety.
They had marginally the better of this encounter but generally both defences were on top against powderpuff attackers and when the keepers were tested, Asmir Begovic and Lee Grant were up to the job.
Town started well and inside the first five minutes, both David Wright and Tamas Priskin had tested Grant, who gathered comfortably, before an angled low free-kick from Grant Leadbitter somehow missed friend and foe alike to be collected by Grant on his line.
Wednesday gradually came back into the game and first tested Begovic on 21 minutes when Jermaine Johnson collected Tommy Spurr's cross, turned inside David Wright but his shot was straight at the keeper.
Town were fortunate not to concede a penalty when Damien Delaney handled a Marcus Tudgay flicked header but referee Andy D'Urso decided it was accidental.
Grant parried a firm drive from Lee Martin, while at the other end Tudgay latched onto a long clearance and fired in a fierce shot which Begovic beat away.
D'Urso let off Lewis Buxton with a stern warning after the already-booked centre half clattered through the ankles of Priskin, before Town ended the half on top with Carlos Edwards shooting wildly over and Jon Walters having a shot blocked from Martin's pull back.
The second half took an age to get going but then burst into life with six decent chances in the space of eight minutes, five of them to an Ipswich side growing increasingly dominant.
Grant saved from an Owen Garvan right-foot volley, Walters had a shot blocked, Priskin's back-heel put sub Alan Quinn through but Grant blocked his effort and Edwards blazed over, while Wednesday sub Leon Clarke mis-kicked in a good position.
The best chance though came when Grant dropped a swirling Leadbitter corner which bounced close to his own line, but as Walters and sub Gareth McAuley tried to bundle it home, Frankie Simek blocked and then cleared to his keeper's relief.
Keane sent on former Sheffield United man Jon Stead and within seconds his low shot brought a fine diving save out of Grant, and although Priskin swept home from Edwards' cross after he latched onto the loose ball, the Hungarian striker was offside.
Clarke got in behind the Town defence onto a long Grant clearance, but McAuley came across to block well, although D'Urso somehow gave a goal-kick.
Tudgay's back-heel found James O'Connor but he screwed his 20-yard shot wide and the last chance of the game fell to Garvan whose low drive from 20 yards was well struck but well held by the diving Grant.