Owls skipper Richard Wood salvaged a priceless point just as SWFC were staring down the barrel of defeat against relegation rivals Coventry.
Wood nodded home Steve Watson's long throw-in on 90 minutes, cancelling out Zavon Hines' first goal for City struck just seven minutes earlier.
The point gained finally moved Wednesday out of the drop zone and extended their productive run of form to just one defeat in ten games.
Brian Laws made two changes from the side that posted a point against league leaders Stoke on Saturday, with Jermaine Johnson coming in at right back for the injured Richard Hinds while Burton O'Brien replaced virus victim Wade Small in midfield.
Wednesday, attacking the Kop, were first to show, winning two corners inside the opening five minutes. Wood went close from the second but his towering header from O'Brien's flag kick sailed narrowly wide.
Coventry were sparked into life and Julian Gray linked up well with Michael Mifsud down the left before the former shot tamely into the midriff of Lee Grant when he could have squared to the on-rushing Robbie Simpson.
But it was Wednesday that came within a whisker of taking the lead on 14 minutes. In-form winger Franck Songo'o flummoxed two defenders before pulling back an accurate feed for Graham Kavanagh, whose drilled effort just fell the wrong side of the post.
Wood and Jay Tabb went into the book as both sides began to up the tempo. Ben Sahar then cut inside from the right channel and thumped in a fierce shot that was deflected wide by Daniel Fox.
Grant made the save of the half moments later, leaping spectacularly to divert Simpson's angled drive for a corner following a smart pullback from Mifsud.
Wednesday were dealt a blow two minutes before half time when Sean McAllister was forced out of the action. Adam Bolder came on for his first outing since extending his loan period from QPR and the last action of a relatively low key half saw Wood head Kavanagh's corner high over the crossbar.
A blinding piece of skill by Songo'o illuminated the start to the second period as Wednesday pressed forward straight after the resumption.
Coventry, though, hit back and were denied a half-hearted shout for a penalty when Richard Duffy tumbled beneath Tommy Spurr's challenge.
SWFC then countered and Songo'o - by far the hosts' likeliest threat on the night - blasted an angled drive that whistled over Kasper Schmeichel's crossbar.
Mark Beevers powered forward from the back on the hour and only some desperate defending prevented the Owls' starlet advancing into the danger zone.
Mifsud tested Grant at the near post in the 64th minute and the keeper was equal to the City striker's snapshot.
Johnson then advanced upfield from his unorthodox right-back berth and almost caught Schmeichel napping with a low drive but the City custodian recovered well down to his left. Then, back in the rearguard, Johnson thwarted Mifsud with an accurate sliding tackle as the Malta international was ready to pull the trigger from ten yards.
Laws introduced latest loan signing Bartosz Slusarski on 83 minutes but it was City substitute Hines - thrown into the fray at the same time - who made the desired impact.
Simpson's hopeful cross was miskicked by Johnson and the ball fell kindly to Hines, who lashed a fierce drive past the despairing Grant to score what seemed to be the winner.
But captain Wood popped up with his first goal of the season right at the last to deny the visitors and, crucially, lift the Owls out of the Championship basement.
Owls: Grant, Johnson, Wood, Beevers, Spurr, Songo'o, Kavanagh (Watson 76), McAllister (Bolder 44), O'Brien (Slusarski 83), Burton, Sahar
Unused substitutes: Burch, Gilbert
Coventry: Schmeichel, Duffy, Fox, Dann, Ward, Tabb, Hughes, Doyle, Gray (Osbourne 90) Mifsud (Hines 75), Simpson
Unused substitutes: Marshall, Hall, Thornton
Referee: Graham Laws
Attendance: 21,110





















