A Matt Holland goal and results elsewhere, left the Yorkshire side back at the bottom of the table.
Wednesday rattled Ipswich with a sharp opening that saw the Town defence hustling Shefki Kuqi out after a dangerous ball from Michael Reddy in the second minute.
And a minute later Ashley Westwood's clever ball forward was flicked on by Lee Bradbury and Kuqi's first-time effort from 20 yards went wide.
But Wednesday's problems mounted after 14 minutes when skipper Darryl Powell hobbled off with an injury and was replaced in midfield by Steve Haslam.
Another half chance fell Kuqi's way, but a volleyed effort from the Finnish striker was saved easily by Andy Marshall.
Ipswich went ahead after they were gifted an opportunity from a sloppy back-pass that gave them their first corner.
Ex-Wednesday midfielder Jim Magilton had the Owls in trouble with a testing corner, Darren Bent reached it with his head and Holland stole in to head it past Paul Evans.
The goal injected confidence into Ipswich but knocked the wind out of Wednesday and Joe Royle's side could have stretched their lead.
Holland angled a shot wide and Darren Bent headed over from a left-flank cross from Matt Richards.
And Wednesday had a let-off seconds before the break when Darren Bent volleyed another chance over from 12 yards.
Wednesday looked for a quick reply after the break, but when Alan Quinn picked out Reddy with a crossfield pass, his shot was blocked and a follow-up from Quinn went into the crowd.
Darren Bent threatened again for Ipswich with a lightning break, as Evans produced an important save.
And Evans denied Holland a second goal for Ipswich with a brave double block after 67 minutes when Holland squeezed through two defenders.
Wednesday boss Chris Turner even made a desperate change late on when he brought on centre-back Tony Crane as a makeshift striker to replace Kuqi, who went off to a chorus of boos from the home fans.