Newcastle trailed seven minutes after the restart in South Yorkshire following Windass' controversial close-range finish, with the goal standing despite replays showing the goalscorer to be in an offside position before the Owls midfielder's composed finish doubled his and the hosts' advantage after the hour mark.
Bruno Guimarães' close-range tap-in swiftly halved the deficit but the visitors were unable to salvage a late fightback, ending their 15-game unbeaten streak across all competitions in the process and exiting at the hands of League One opposition for a second consecutive term following last year's loss against Cambridge United.
Eddie Howe made eight changes from the side which claimed an impressive 0-0 draw at Premier League leaders Arsenal on Tuesday evening as Swedish forward Alexander Isak was handed a first start since September while Martin Dúbravka started in-between the sticks, the Slovakian's first competitive outing for the Magpies since May.
There were also starts for club captain Jamaal Lascelles - making his 200th in all competitions for United - as well as Matt Ritchie, Jacob Murphy, Elliot Anderson, Javier Manquillo and Jamal Lewis.
It was the hosts, occupying second spot in League One, who created the opening goalscoring opportunity as Owls captain Liam Palmer intercepted a United throw-in and drove towards goal before firing a low effort wide of the left-hand post.
Isak, who joined the Magpies from La Liga outfit Real Sociedad last summer, went close to breaking the deadlock in the opening stages as the 22-year-old rose high from Javier Manquillo's teasing cross from the right flank before the striker's header was pushed away by Wednesday goalkeeper Cameron Dawson before the ball was cleared out for a corner.
Newcastle were fortunate to remain on level terms shortly after as Elliot Anderson's pass towards his own goal was cut out by Josh Windass but his first-time shot was directed wide of Dúbravka's goal.
Isak and Manquillo combined with another chance in front of goal as the latter threaded a neat pass into the striker's path inside the penalty area but his powerful drive towards goal was blocked by Dawson.
The Magpies almost fell behind in misfortunate fashion as Palmer's teasing cross from the right wing forced Sven Botman into flicking the ball out for a corner, which flew narrowly wide of the far left-hand corner.
With the half-time whistle approaching, Murphy squandered an opportunity to send the Premier League side ahead at the break after racing onto Matt Ritchie's lofted pass but his attempt at lifting the ball over Dawson directed past the target.
In the second-half, Botman targeted his first goal for the Magpies since joining from Lille in July 2022 as the Dutch centre-back was allowed time from distance before his long-range effort flew past the right-hand post.
In the 52nd minute, Newcastle's hopes of a seventh consecutive clean sheet were ended as Sheffield Wednesday took the lead through Windass as the midfielder latched onto Dennis Adenirian's pass inside the box before directing the ball into the net and, with no VAR in operation at Hillsborough, the goal stood despite with the midfielder situated in an offside position.
Elliot Anderson missed a golden chance to draw the visitors level as the 20-year-old latched onto a loose ball inside the box following Ritchie's cross but his attempt was blocked from point-blank range by Dawson.
Dúbravka was on hand to prevent the League One side doubling their advantage as the 33-year-old goalkeeper beat away Windass' stinging effort.
In the 65th minute, Newcastle fell further behind as Windass raced in behind the United defence before slotting the ball beyond Dúbravka.
Howe made a triple substitution as Miguel Almirón, Joe Willock and Bruno Guimarães were introduced to the field and it was the latter, in the 69th minute, who provided a lifeline for United as the Brazilian midfielder, appearing offside also, was on hand to place the ball into the net inside the six-yard area.
Windass went incredibly close to restoring Wednesday's two-goal cushion and netting a hat-trick after crashing a long-range free-kick off the crossbar.
Chris Wood, introduced from the bench in place of Isak at the half-time break, ought to have drawn United level in the closing stages as the New Zealand international was teed up by Joelinton inside the box, following Kieran Trippier's delightful pass, but the Kiwi forward placed his attempt over the bar.
