Shefki Kuqi was on the bench despite scoring the winner against Watford last time out. His place was taken by Craig Beattie, while Cedric van der Gun also found himself in the dugout as Paulo Sousa continued his policy of resting players.
Both sides made a bright opening with David Cotterill forcing Lee Grant into a fourth minute save, while at the other end Leon Clarke's lob was clutched under the cross bar by Dorus de Vries.
Darren Pratley worked his way into the area in the 14th minute but he was unable to bend his shot beyond Grant.
By midway through the half the Swans were beginning to take control and Pratley's pace through the middle was causing the Wednesday defence problems.
Yet it was the visitors who went closest to opening the scoring when Jermaine Johnson's deflected shot just before the half hour landed on top of the Swansea net.
As half-time approached Wednesday mounted a few attacks but the Swans defence cleared the danger and the teams went in level.
Kuqi started the second half in place of the ineffective Beattie while van der Gun replaced Tom Butler.
Kuqi was in the action straight away as he met a Pratley cross first time only to rifle the ball just wide of the Wednesday post.
Luke Varney fired across goal in the 54th minute but no one was on hand to touch the loose ball into the Swansea net.
The busy Pratley met a van der Gun cross in the 62nd minute but his snap header flew over the visitors crossbar as the Swans began mounting pressure in an effort to take all three points.
Tommy Miller sent in a rocket shot that pole-axed Ashley Williams five minutes later but the ball was cleared by the home defence.
Wednesday keeper Grant needed lengthy treatment after preventing Kuqi getting through on goal and then Lee Trundle replaced Cotterill in a last throw of the dice for the Swans.
With five minutes remaining, Trundle mishit a shot that went across goal and then van der Gun found himself in a good position but each time the Wednesday defence recovered to clear.
Even with seven minutes of time added on, the Swans were unable to pierce a dogged Wednesday defence and two valuable home points were lost.