The forward's miss-hit volley from Joe Mattock's corner after 12 minutes somehow went in to reward the hosts for their early pressure.
The Owls almost took the lead after two minutes but Gary Madine headed Antonio's inviting cross inches wide.
Jermaine Johnson, operating just behind Madine, then charged forward and let fly from long range and goalkeeper Scott Gallacher did well to hang on to his fierce shot.
Rangers had offered little as an attacking force but against the run of play they threatened three times in the space of five second-half minutes.
Nicky Law, formerly of Sheffield United and Rotherham, dragged a shot wide from an acute angle. The diminutive midfielder then played in Andrew Little, who stung the palms of the goalkeeper. Shortly after the hour mark, Little then flashed a shot narrowly wide.
But back came Wednesday and Madine, on the stretch, stabbed Chris Maguire's teasing cross over the top.
An unstoppable strike from Marc-Antoine Fortune gave Wigan a 1-0 victory over Morecambe at the Globe Arena.
Fortune's goal came 15 minutes from time from a Latics counter-attack. He cut inside Tony Diagne and fired a thunderous right-foot shot from just outside the area past goalkeeper Barry Roche's outstretched left hand.
Summer signing Grant Holt should have put the FA Cup holders ahead early on but lifted his shot wide when one-on-one with Roche, who soon had to deny Wigan skipper Emmerson Boyce.
Williams tested Carson with another set piece after the break before Fortune's strike settled the game.
Posh led for 45 seconds in the second-half thanks to a cool finish by Swanson following a superb pass from Lee Tomlin.
However, the Hornets equalised in the 61st minute following some brilliance of their own as McGugan thundered a 25-yard free-kick against the crossbar before Troy Deeney converted the rebound from close range.
Bristol City beat Reading 1-0 after a late goal from transfer-listed winger Albert Adomah.
Adomah produced an excellent finish following a good team move and his solitary strike proved the difference on the night.
The Royals should have at least drawn the game, with Chris Gunter and Nick Blackman spurning close-range chances in the closing stages.
Blackman - one of seven second-half changes - saw a header cleared off the line and could not keep the rebound down. Gunter then smacked well over from the edge of the six-yard box right on full time.
Leicester preserved their unbeaten pre-season record with a confident display in a 0-0 draw against a spirited York side at Bootham Crescent.
Nigel Pearson's team dominated possession for long periods against their League Two opponents, whose solid defending held Leicester at bay despite Danny Drinkwater seeing a shot strike the post in the first half and David Nugent having two efforts cleared off the line.
However with an exciting home tie against AS Monaco beckoning on Saturday at the King Power Stadium and a new season around the corner, Pearson will have been pleased to see his charges come through a tough run out unscathed.
Wednesday’s pre-season results
Featuring a Premier League side
Melbourne Victory 0-2 Liverpool
South China 0 Manchester City 1
Forest Green 3-4 Cardiff City
Sheffield Wednesday 1-0 Rangers
Morecambe 0-1 Wigan Athletic
Billingham Syn 0-3 Middlesbrough
Bristol City 1-0 Reading
York City 0-0 Leicester City
Peterborough 1-1 Watford
MK Dons 4-3 Rayo Vallecano
Stocksbridge Park Steels 1-3 Rotherham United
Leyton Orient 2-1 New York Cosmos