The hosts took the lead after 90 seconds then added another just before the hour-mark.
Daniel Stendel kept the same 18-man squad for the opening day win over Fulham and, while there were glimpses of that excellent performance, the Owls had the better of the game and created more chances.
The Reds had plenty of the ball in the first half and looked confident, creating some decent opportunities, but were always vulnerable to being passed through at the back.
Barnsley got off to a terrible start as Cameron McGeehan lost the ball deep in his half and, after ex-Red Kadeem Harris’ shot was blocked, Owls deadline day signing Jacob Murphy was clean through on goal and beat Sami Radlinger ten yards out.
Alex Mowatt had the visitors’ first attempt on goal but his 35-yard free-kick was easily saved while Murphy whipped a free-kick wide from 25 yards.
Luke Thomas had the chance to make it two goals in as many games when a Toby Sibbick cross was half-cleared and fell to him 15 yards out but his tame effort dribbled wide.
Wednesday almost added a second on 33 minutes but Julian Borner nodded a right-wing free-kick straight at Radlinger who then made an even better save seconds later as Adam Reach was put clean through by Steven Fletcher but saw his shot blocked in a one-on-one situation.
Barnsley’s Mallik Wilks then fizzed a shot from the left of the box across the box, which was a few feet away from an equaliser against the run of play. The Reds then had a much better chance to level when stand-in Wednesday goalkeeper Cameron Dawson made a point-blank save from Cauley Woodrow five yards out after McGeehan headed down a Wilks cross.
The home side were more dominant in the second half and could have won by more than two goals. The Owls were furious seconds after the break when Radlinger rushed out of his box and appeared to handle the ball but no free-kick was given by referee Tony Harrington who also felt Mads Andersen had not fouled Murphy in the box soon after.
Borner then headed over another chance from a right-wing Reach cross then Harris shot weakly at Radlinger on the right of the box after the away defence was again opened up by a long ball.
Barnsley almost levelled on 57 minutes but Mowatt fired over on the volley at a tight angle on the left of the box following a scramble after a corner.
The hosts doubled their advantage on 60 minutes when they worked the ball from the right wing into the centre where veteran striker Steven Fletcher fired a left-footed strike into the bottom right corner.
Stendel responded by bringing on Conor Chaplin and Mamadou Thiam for captain Mike Bahre and Wilks. Thiam almost pulled one back midway through the second half when Wednesday lost the ball deep in their half and it was worked to the Frenchman whose deflected shot was cleared off the line by Borner.
Fletcher fired a 25-year free-kick just over the bar then Mowatt limped off for Barnsley and was replaced by Callum Styles.
Radlinger again made a one-on-one save from Massimo Luongo – who had just come on for his debut – with ten minutes to go after he exchanged passes in the box with McGeehan who again lost the ball in a dangerous area.
Barnsley (4-4-1-1): Radlinger, Sibbick, Andersen, Diaby, Cavare; Thomas, McGeehan, Mowatt (Styles 77), Wilks 7 (Thiam 60); Bahre 6 (Chaplin 60), Woodrow. Unused: Collins, Styles, Halme, B Williams, Miller. Yellow cards: McGeehan.
Wednesday: Dawson; Odubajo, Lees, Borner, Palmer; Reach, Hutchinson, Lee (Luongo 80), Harris; Murphy (Pelupessy 74), Fletcher (Rhodes 77). Owls subs: Jones, Fox, Nuhiu, Forestieri. Goals: Murphy 2, Fletcher 59. Booked: Borner.
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15:03pmGOAL!
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16:08pmYELLOW CARD
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16:19pmGOAL!
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16:48pmYELLOW CARD
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16:50pmADDED TIME
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