Wilson could consider his team somewhat unfortunate not to share the derby spoils. Having fallen behind to Dejan Stefanovic's goal midway through the first half, Barnsley responded positively and were worth their equaliser by Di Canio's only rival as the game's most influential performer, Neil Redfearn.
A corner count of 13 to one in the visitors' favour gives an accurate impression of their ascendancy between the half-hour mark and the final 10 minutes. Then, much as they had done when losing 3-2 to Leeds nine days earlier, they tired visibly.
For Wednesday, seemingly satisfied with a point after their least impressive performance since Atkinson returned in place of David Pleat, it was all the encouragement they needed. Mark Pembridge quivered Barnsley's bar, while Andy Booth had a shot scrambled off the line by Nicky Eaden.
Just when Wilson must have felt his players had done enough to clamber above Everton, they were undone by a throw-back to Wednesday's route one days.
Kevin Pressman launched a towering kick from the back, which dipped out of the swirling rain before skimming off the head of Adie Moses. Di Canio was on to the ball in a flash, gliding round Lars Leese before sidefooting his ninth goal since a summer transfer from Celtic.
There was a case for arguing that the Italian should not have been on the pitch by then. Ten minutes earlier, he raised his arms in a fracas with Darren Sheridan. Mr Willard showed the yellow card; other players, most recently Coventry's Gary Breen, have been sent off for less.
A foul on the ubiquitous Di Canio had earned the free kick which led to Wednesday's 19th-minute breakthrough. When the ball was curled in by Benito Carbone, Barnsley were confused by Booth's muscular presence. Stefanovic, up from defence, pounced to prod in his first goal of the season.
Following a reprieve when Ian Nolan's swerving volley passed narrowly wide, Barnsley's brisk counter-attacking deservedly hauled them level within 10 minutes. Redfearn's slide-rule free kick, after Guy Whittingham had bundled over Ashley Ward, hit the inside of the far post on its way in.
Another set-piece created havoc at the back for Barnsley, Di Canio's drive breaking off a defender to leave Booth with an angled shot which cannoned to safety off Leese's legs. But Redfearn had been encouraged by his seventh goal of the season and began to dominate proceedings.
His cunningly flighted corners enabled them to establish second-half ascendancy. Jovo Bosancic headed over from one, yet in a reversal of their earlier roles, Wednesday almost profited from a swift break-out. Petter Rudi, whose languid, loping stride stirs images of Chris Waddle among the Wednesday faithful, came close to restoring their advantage after a one-two with Whittingham. Given a similar opportunity, Di Canio was ruthlessness personified.
Sheffield Wednesday: (4-4-2): Pressman; Nolan, Walker, Stefanovic, Pembridge; Whittingham, Collins, Carbone (Hyde, 66), Rudi; Di Canio, Booth. Substitutes not used: Blondeau, Humphreys, Magilton, Clarke (gk).
Barnsley: (3-5-2): Leese; Moses, Appleby (Bullock, 90), Krizan; Eaden, Redfearn, Bosancic, Sheridan, Barnard; Liddell (Hendrie, 86), Ward. Substitutes not used: Marcelle, Hristov, Watson (gk).
Referee: G Willard (Worthing).Reuse content