The Owls claimed three points at the KC Stadium on Saturday evening beating Hull City 3-1.
Reda Johnson opened Wednesday’s account in the first half, heading into the net from Rhys McCabe’s free kick.
Robert Koren equalised for the hosts eight minutes from time but Wednesday were soon back in front and in strange circumstances.
Miguel Llera’s corner in front of the travelling Owls contingent was not dealt with by Hull keeper Eldin Jakupovic, who dropped the ball over his own goal line.
Michail Antonio than capped a superb display by Wednesday on the break in the last minute as the forward rounded the Hull goalkeeper before finishing into an empty net.
There was still time for a late scare though when the Tigers were awarded a penalty for Jeremy Helan’s foul on Jay Simpson – the same man stepped up from 12 yards but Kirkland made a fine save down to his right – adding to Hull’s misery.
Dave Jones made six changes from last weekend’s FA Cup-tie against MK Dons and included Giles Coke in the starting line-up, who made his first Owls league appearance of the term.
Hull went into the clash in excellent form unbeaten in nine but it was Wednesday that threatened first less than five minutes into the contest.
Antonio had the Hull rearguard back peddling with a mazy run from the left before teeing up Jermaine Johnson who brought a fine save from Jakupovic after unloading outside the area.
Abdoulaye Faye was then perhaps fortunate to escape without punishment after a firm challenge on Jermaine Johnson just past the halfway line.
The game then exploded into life on the 25-minute mark when the visitors hit the front through Reda Johnson.
Jeremy Helan did well to win a free kick on the edge of the area on the left and McCabe delivered a fine ball into the box for the Benin international to head beneath Jakupovic.
The Owls then had the chance to add to their early lead when Jermaine Johnson raced into the Hull box and squared for Antonio, whose first touch gave Jakupovic the chance to make a save and send behind for a corner.
As the game approached the interval, both sides had chances to hit the back of the net.
First, Jermaine Johnson fired a fierce shot on target from distance that required a smart save from Jakupovic.
Stephen Quinn then saw his near post header flash wide for the hosts before Tigers skipper Robert Koren was thwarted by Kirkland after springing the offside trap to go one on one with the ex-Liverpool keeper.
Hull inevitably came out for the second half with the bit between their teeth and Sone Aluko found space down the right of the penalty area but blasted over when he might have done better.
Then there was controversy on 58 minutes when Coke put the ball in the back of the net from a tight angle but the strike was ruled out for an earlier infringement.
With a group of Wednesday players still celebrating off the field, Hull quickly took the free kick and broke upfield only to lose possession, which landed at the feet of Jermaine Johnson, who forced a fine save at the near post by Jakupovic.
The Owls had looked good value for the lead in East Yorkshire and with the clock against the Tigers, Wednesday continued to be resilient at the back while also remaining a threat going forward.
But with eight minutes to go Hull hauled themselves back into the game.
Ahmed Elmohamady whipped in an accurate ball from the right for Koren to nod past Kirkland.
That set back did not deter Wednesday, who immediately restored their one-goal advantage.
Llera’s deep corner was seemingly dealt with by Jakupovic but the Hull keeper somehow took the ball over his goal line, and with the referee’s assistant well-placed, the goal stood and the Owls were 2-1 up.
As Hull pressed for a late equaliser, Wednesday wrapped up proceedings on the break through Antonio.
The ex-Reading man carried the ball from the half way line before rounding substitute keeper Mark Oxley and finishing into the empty to cap an excellent away display by the Owls.
Deep into added time, Jay Simpson was awarded a penalty for a challenge by Helan. The same man stepped up to take the spot kick but Kirkland was not to be beaten and saved down to his right as Wednesday posted three points on the board.
Hull: Jakupovic (Oxley 90), Chester, Hobbs (Proschwitz 79), Evans (Simpson 66), Koren, Faye, Aluko, Elmohamady, Quinn, Brady, Meyler
Substitutes: Rosenior, Cairney, McShane, Bruce
Owls: Kirkland, Buxton, R Johnson, Gardner, Antonio, J Johnson (Sidibe 81), McCabe (Semedo 46), Lee, Helan, Coke, Llera
Substitutes: Bywater, Taylor, Madine, Mattock, Corry