Marcus Tudgay and Madjid Bougherra scored in either half as Ipswich were twice caught out at set-plays - the first from their own corner, the second an unmarked header from a Wednesday corner.
In between the goals, Ipswich huffed and puffed, but squandered the best of the opportunities they created, and indeed the closest they came to a goal was when Lee Bullen headed against his own post late on.
Wednesday started well and John Hills whipped in a quick free-kick which Deon Burton cleverly headed down to strike partner Tudgay, whose firm strike drew a good diving save from Shane Supple.
Chris Brunt put in two dangerous corners, one of them headed away from close to the goal-line by Sylvain Legwinski, the other flashing across the face of goal, before the Owls went ahead on 11 minutes.
It came from Ipswich's first corner as Wednesday broke swiftly upfield before Wade Small fired in a low cross and Tudgay timed his run perfectly to slide home his sixth goal in five games.
Bougherra blazed over from a quickly-taken Kenny Lunt free-kick before Ipswich began to build up a head of steam as half-time approached.
Matt Richards picked out Alan Lee perfectly, but the striker - with eight goals in his last eight games - side-footed wide from six yards, Mark Noble volleyed wide from 25 yards and then Gary Roberts crossed for Richards to blaze over from six yards.
Brunt forced a save out of Supple, albeit with a weakly-struck effort from 20 yards as Wednesday started the better after the break, as the Ipswich sting looked to have been drawn by the interval.
Sub Jon Macken shot into the side-netting after turning sharply onto a Lee flick but Wednesday then came close with a Brunt chip which was just ahead of Small and floated past the far post.
Supple held an ambitious Tudgay overhead kick before Town sub Darren Currie crossed deep for skipper Jason De Vos to head dangerously across goal, where Mark Crossley grabbed the ball at the second attempt.
Bullen did well to clear a dangerous Roberts cross as Lee closed in on goal before Town mustered a first effort on target after 71 minutes, although Crossley had little trouble with Richards' 25-yard free-kick.
Macken flicked a header wide and possibly denied the better-placed Lee behind him from a Roberts cross, before Wednesday got the killer second goal.
Lunt drifted over a corner and Bougherra lost Fabian Wilnis at the far post to thump a fierce header past the helpless Supple from six yards.
Tudgay should have made it three a minute later when Burton picked him out after charging down an Alex Bruce clearance, but Supple spread himself well to make a fine save.
Town came close to a consolation late on as Bullen sent a diving header against his own post from a Roberts cross, and then Lee had a header tipped over by the under-worked Crossley, but the Owls deservedly held on for all three points.