The Swans fielded the side victorious at Plymouth, with Gorka Pintado on the bench despite scoring in the midweek Carling Cup win.
Both sides pushed forward in the opening stages with Etienne Esajas shooting straight at Dorus de Vries for the Owls and Tom Butler working his way in for the Swans, only to have his shot blocked.
Butler and Mark Gower were given plenty of ball out on the flanks, but their crosses failed to trouble the visitors' defence.
Gower almost broke the deadlock in the 28th minute but Lee Grant went low to tip his shot round the post.
Ferrie Bodde picked up a loose ball 25 yards out in the 36th minute to thunder a shot into the back of the net to give the Swans a deserved lead.
It took two superb tackles inside the area by Wednesday defender Mark Beevers to prevent Jason Scotland and then Gower from adding to the Swans' interval lead.
The home side forced a corner in the first minute of the second period and when they were awarded a free-kick out wide Ashley Williams raced in, but his header went high over the bar.
In the 64th minute another header from Williams thudded against the cross-bar as the one-way traffic continued with the Owls barely having a touch of the ball so dominant were the Swans.
Totally against the run of play Wednesday equalised in the 70th minute when Marcus Tudgay chipped into the area and Steve Watson, who had only been on the field 30 seconds, headed into the corner of the net.
One minute later Gary Monk missed an open goal at the other end when he headed wide from a cross by Gower.
Owls' defender Tommy Spurr then saw a cross strike the home woodwork with de Vries beaten as the game opened out and both sides went looking for victory.
In time added on Febian Brandy struck the base of the post but the Swans had to be content with only a point.