The Senegal striker was recalled to the Newcastle starting XI in place of Emmanuel Riviere and delivered once again with a fine double.
Cisse had come off the bench and netted twice to salvage a 2-2 draw with Hull City a fortnight ago, and replicated the feat with two clever finishes at the Liberty Stadium on Saturday.
Wilfried Bony - who came in to Swansea's team at the expense of Bafetimbi Gomis - opened the scoring in the 17th minute for the hosts.
Cisse levelled shortly before half-time, but Wayne Routledge looked to have condemned his former club to another defeat when he restored Swansea's lead.
However, Newcastle refused to accept their fate and Cisse proved their saviour, stealing in 15 minutes from time to seal a share of the spoils and perhaps ease some of the pressure on Pardew in front of watching owner Mike Ashley.
Newcastle remain without a Premier League win this season, while Swansea have now gone four top-flight games without victory after winning their first three in the 2014-15 campaign.
It took until the 16th minute for Newcastle to craft the game's first real opportunity as Gabriel Obertan – recalled alongside Cisse as one of two changes by Pardew - fired wastefully wide.
Newcastle were punished almost immediately by Bony, who slotted beyond Tim Krul following neat link-up play with Gylfi Sigurdsson.
The visitors dominated possession in their search for an equaliser but lacked a cutting edge for much of the first half.
For all Newcastle's industry, Swansea should have doubled their lead in the 34th minute, midfielder Ki Sung-yueng somehow heading wide from Sigurdsson's free-kick with the goal at his mercy.
Bony was then denied by a brilliant save from Krul, the Netherlands shot-stopper diving low to his left to keep out a volley.
Swansea paid the penalty for their profligacy in the 42nd minute when Cisse cleverly turned home Obertan's low delivery at the near post.
Yet Garry Monk's men retook the lead five minutes after the restart through Routledge.
The winger latched on to a pass from Sigurdsson and lifted the ball over Krul following more haphazard defending from the visitors.
In an attempt to regain momentum, Pardew brought on Riviere to partner Cisse up front, with Jack Colback making way.
Swansea continued to create the better chances, Krul pulling off another wonderful save to prevent Bony from claiming a second.
Krul was then rewarded for his heroics by Cisse, who prodded home a pinpoint right-wing cross from substitute Sammy Ameobi.
Sensing a spectacular comeback, Newcastle threw bodies forward in an ultimately fruitless search for a winner, Cisse spurning the chance for a hat-trick late on as he shot over the crossbar with the goal seemingly gaping.
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