17 minutes into the game, Gylfi Sigurdsson played a wonderfully-weighted ball through to Wilfried Bony, who placed it past Tim Krul to give the Swans the lead.
Garry Monk’s side could have doubled the lead when Bony volleyed the ball towards the bottom-right corner, but the Magpies’ Dutch keeper did magnificently to turn the ball around the post.
Moments before half-time, Cisse grabbed an unexpected equaliser after he prodded a Gabriel Obertan cross beyond a stranded Lukasz Fabianski.
However, just five minutes after the break, former Magpies winger Wayne Routledge lifted the ball over a sprawling Krul to put the home side back in front.
Despite Swansea looking good value for their lead, Newcastle broke on the counter attack and Cisse levelled from five yards after some superb play from substitute Sammy Ameobi.
Both sides had chances to win the game, but it finished all-square in South Wales – a result that will undoubtedly give Pardew more time as Newcastle manager.
The Newcastle fans voiced their displeasure at both Pardew and owner Mike Ashley – who was present at the Liberty Stadium – regularly during an entertaining contest, with the visitors desperately short of confidence and still seeking their first win of the league campaign.
Swansea had made their best start to a Premier League campaign but they had gone three games without a win and it showed as both sides took time to settle.
An early spell of shadow boxing ended when Obertan fired just wide and the chance seemed to spur Swansea into action at the other end.
Bony played Ki Sung-yueng’s pass to Sigurdsson and a simple one-two saw the Ivorian bear down on goal and slot home past Krul for his first goal since scoring for the Ivory Coast at the World Cup in Brazil.
It was also Sigurdsson’s fifth assist of a productive Premier League season but from a Newcastle perspective their defence had been breached far too easily.
Shelvey’s delicate chip cleared Krul’s crossbar following some slick Swans approach play and the hosts almost doubled their advantage after 38 minutes.
Another free-flowing move had threatened to break down but Sigurdsson helped it onto Nathan Dyer and he beat his marker Paul Dummett with ease.
Dyer’s cross found Bony but Krul produced an excellent save to divert his volley wide at the expense of a corner.
Newcastle had barely functioned as an attacking force but two minutes before half-time, Obertan got the better of Neil Taylor and Cisse stole across Ashley Williams at the near post to beat Fabianski in the Swansea goal.
Swansea responded immediately with Bony seeing a shot blocked by his skipper Williams before driving a fierce effort over, but Newcastle’s luck held only until five minutes into the second half.
Sigurdsson held off Moussa Sissoko, perhaps too forcefully for Pardew’s liking, to slip a pass into Routledge’s path with Dummett playing him onside in the left-back position.
Krul came rushing off his line but Routledge nonchalantly beat him with a delightful chip to restore Swansea’s lead.
Newcastle were making little attacking headway and came close to conceding a third when Sigurdsson’s back heel found Bony who just failed to keep his chip under Krul’s bar.
Bony was almost on the scoresheet again when he met Dyer’s centre sweetly and Krul pulled a save from right out of the top drawer.
And that stop proved more important moments later when substitute Ameobi evaded the challenge of Federico Fernandez and crossed for Cisse to volley home from close range.
Cisse almost completed his hat-trick with 10 minutes remaining when Emmanuel Riviere’s blocked shot fell to him inside the six-yard area but he couldn’t maintain his balance and the chance was lost.