Bodde's superb strike had the Liberty Stadium in raptures
Substitute Steve Watson salvaged a point for Sheffield Wednesday after Ferrie Bodde's stunning Swansea opener.
Bodde stole Owls possession, strode forward, and unleashed a dipping 25-yard strike across the face of goal and low into Lee Grant's left-hand corner.
Ashley Williams hit the post, but the Swans lost concentration as Brian Laws sent on three subs, Watson unmarked to head in Marcus Turgay's cross.
Febian Brandy's glancing header from Bodde's cross hit the post late on.
Swansea manager Roberto Martinez: "We controlled the game for 90 minutes and created enough chances.
"We reduced Sheffield Wednesday to two attempts in the second half and we were punished.
"I am pleased with the performance, but I feel we dropped two points.
"The amount of chances we created, we should have won the game."
Sheffield Wednesday manager Brian Laws: "To come in 1-0 down at half-time, I was quite pleased because our performance made it easier for Swansea as we were poor today.
"I don't believe many people will come here and take many points off Swansea if they play like that.
"I'll take a point but I'm sure Swansea think they lost two points.
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