Wilfried Bony’s 15th-minute strike had handed the hosts a well-earned lead but Jedinak, who entered the field with a cricket bat and cap in a mark of respect to the late Australian cricketer Phillip Hughes, levelled proceedings to grab a point for his side.
Swansea started the day in seventh place with manager Garry Monk saying the next nine games would define their season – whether they could make a challenge for a European place or be looking over their shoulder at the teams below them.
The game appeared to be a formality in the opening exchanges with Swansea applying a sustained onslaught on the Palace area in a dominant opening spell.
It took Swansea just a matter of minutes to get into their usual rhythm of possession football and, undeterred after having a penalty appeal waved away by Martin Atkinson when Neil Taylor went down in the area, Jefferson Montero and Wayne Routledge caused mayhem down Palace’s flanks.
Bony twice went close as the Swans looked to open the scoring and Gylfi Sigurdsson sent over an angled free-kick before the home side took a deserved 15th minute lead.
After a series of spurned opportunities, Swansea’s in-form striker duely obliged, with Bony coolly slotting past Julian Speroni in the Palace goal after he turned and swivelled at the edge of the box following Sigurdsson’s neat interplay.
It was the Ivorian’s 18th Premier League goal of the calendar year – the best record in the division.
It seemed a matter of time before Swansea would build on their lead but the game turned just over 10 minutes later when, against the run of play, the visitors ventured forward for the first time though Yannick Bolasie, with the Congo international winning the first in a succession of corners.
Jonjo Shelvey – recalled into the starting XI in place of loan signing Tom Carroll – got on the wrong side of Marouane Chamakh in a congested penalty area after the second corner and the Palace forward fell to the floor.
Referee Atkinson adjudged the England midfielder to have fouled the Moroccan and pointed to the spot, thereby giving the visitors an unlikely route back into a game in which they had been outplayed for the most part.
Jedinak stepped up and fired straight down the middle to draw his side level, with the equaliser appearing to turn the tide and give Palace a foothold in the game, while also acting to dampen the promising start the Swans had made to the game.
Bolasie finally got into the game and linked up with Chamakh – who was lucky to stay on the pitch after a succession of repetitive fouls and a handball – as Palace ended the half noticeably better than which they started it.
Chamakh went into referee Atkinson’s book for scything down Neil Taylor and he was perhaps fortunate to still be on the field as he had escaped a blatant show of dissent in the opening stages when throwing the ball down in disgust at the award of a Swansea free-kick.
Bolasie clipped the Swansea crossbar from 20 yards with referee Martin Atkinson adjudicating that Fabianski had got a touch on it – but Palace were sent a warning that the threat from the home side was not over.
Slick passing play between Bony and Sigurdsson opened up the space for Routledge to run through unattended but his left-foot shot lacked power and Speroni saved comfortably.
The Moroccan still emerged for the second half despite the fact he was walking a very thin line and Palace were encouraged by Jedinak firing at Fabianski and Bolasie having his shot deflected wide.
Swansea had wrestled control back for the most part but openings were not too forthcoming, although Sigurdsson’s effort 12 minutes from time was too close to the far post for Palace’s comfort.
Sigurdsson was the most likely player to grab a winner but when he blazed over after taking Angel Rangel’s pass Palace’s point was secure.
It was Palace’s resilience in defence, and their ability to prevent Swansea from dominating the game as they had in the first half, which ultimately decided the outcome of the game.
Soccer Saturday reaction – Paul Merson
“Swansea started very well and got a great goal by Bony; all in one movement he turned and ‘bang’ put the ball in the corner. It was a great start. But there was a blessing in disguise for Crystal Palace. Gayle got injured and McArthur came on. If that didn’t happen, the game would have been over at half-time.
“They were all over the place. But when James McArthur came on, Chamakh went up front, Palace got more men behind the ball and they were much, much better. That for me was the game changer.
I don’t think it was a penalty for the equaliser, though. Chamakh turned, Shelvey didn’t touch him and the ref gave a penalty. But Jedinak scored and it’s 1-1.”