The game was stretched in the final half hour and Swansea's Darren Pratley and the Owls' Leon Clarke could have won the match for their sides.
Swansea started the game on the front foot with a prolonged period of possession and winger David Cotterill fired in a 25-yard drive in the third minute which Wednesday goalkeeper Lee Grant managed to scramble clear.
In the 18th minute Craig Beattie rose above the Wednesday defence to meet Thomas Butler's cross but could not direct his header goalwards.
Swansea were struggling to create clear chances despite their patient play and in the 28th minute Wednesday were almost in front.
Leon Clarke hooked the ball along the edge of the 18-yard box and Jermaine Johnson fizzed a volley that was deflected onto the roof of Dorus de Vries' net.
Swansea failed to re-establish their rhythm before the interval and Johnson's mazy runs were proving to be a constant problem.
Beattie was replaced by Shefki Kuqi at half-time and the big Finn almost had an immediate impact when he smashed a volley narrowly wide from 18 yards.
Johnson continued to cause the Swans problems and he spun full-back Angel Rangel with ease but Clarke could not latch onto his cut back.
Pratley then spearheaded a Swansea counter attack which resulted in Grant saving at the feet of substitute Cedric van der Gun.
The end-to-end nature of the contest continued and when Wednesday's Luke Varney engineered some space to flash the ball across Swansea's goal, Clarke was inches away from breaking the deadlock.
In the 62nd minute Swansea had the best chance of the game when Van der Gun whipped in a peach of a cross which Pratley headed over from six yards.
Tommy Miller's venomous strike from inside the area looked bound for the Swansea net in the 70th minute, but it was blocked by Ashley Williams, who was left prostrate on the pitch.
Substitute Lee Trundle could have won it for the home side with five minutes to go when Mark Gower found him six yards from goal, but he slashed horribly wide.
Swansea were ending the game as they started and Williams headed a Gower cross past the post with the goal at his mercy in the final minute.
Clarke again had the chance to grab three points for Wednesday, but he miskicked when well placed in the area after Miller got the better of Alan Tate.