The striker struck in each half to stun Brian Laws' side, whose run of five wins in seven games has pushed them to the edge of the play-off spots.
Wednesday, fresh from a 3-0 derby win over Barnsley, tested Boaz Myhill in the opening minutes, midfielder Glenn Whelan powering in a low strike from 25 yards that was pushed round the post by the diving keeper.
A looping cross from Frank Simek almost found Deon Burton minutes later before Hull snatched the lead in the 10th minute, Andy Dawson threading the ball to Barmby who raced to the edge of the box before beating the exposed Mark Crossley with a low shot into the far corner.
Jon Parkin powered a header over the bar from eight yards before the big striker squandered a half chance as he ran on to Simek's poor clearance but hammered the ball high and wide from 12 yards.
Hull carved out another opening with Wednesday still reeling, Barmby picking out Craig Fagan whose stinging shot was only half stopped by Crossley before taking a deflection for a corner.
Wednesday caught the Hull defence sleeping in the 25th minute, Myhill producing a one-handed stop to keep out Marcus Tudgay before a Simek strike from 25 yards lashed into the sidenetting.
Burton levelled matters in the 53rd minute with a neatly taken goal, twisting past two tackles before planting a low right-foot shot beyond Myhill's reach from just inside the area.
Hull suffered a blow in the 59th minute when the injured Myhill limped off to be replaced by sub keeper Matt Duke.
As Wednesday looked for a second Chris Brunt passed inside to Burton, who curled the ball the wrong side of the far post.
Burton almost snatched an equaliser as he connected with a Brunt cross only to see his right-foot effort blocked and in a nail-biting finish Dean Marney was a fraction away from adding a third - just failing to connect with Dawson's cross from the left flank.