The in-form Senegal striker opened the scoring with a low shot in just the fifth minute before sealing the win in the 69th minute by lofting over Michel Vorm for his ninth goal in just eight games.
Swansea, who suffered a third straight league loss for the first time since 2004, at times enjoyed almost a monopoly on possession but their lack of a genuine cutting edge was cruelly exposed by the Magpies.
Gylfi Sigurdsson, the Premier League Player of the Month for March, had their best chances but it was Cisse whose goalscoring prowess again stole the headlines.
His Liberty Stadium double was the former Freiburg man's third in consecutive games, and his form since his arrival in January has been key in Newcastle's best league run since April 2006.
The contest between Alan Pardew and Brendan Rodgers, who left top scorers Danny Graham and Scott Sinclair out of his starting line-up, had been tipped as a clash between two potential winners of the manager of the season award.
But the ultimate difference between the sides was highlighted inside the opening five minutes.
Sigurdsson had an early chance for the hosts but he could only screw his shot wide after Nathan Dyer had dispossessed Demba Ba.
And Newcastle showed how it should be done as they stunned the home crowd by taking the lead.
Yohan Cabaye produced a classy first-time through-ball to find Cisse and although Swansea keeper Vorm got a hand to the striker's low effort, he could not keep it out.
Swansea responded as Angel Rangel blazed high and wide after Dyer's neat dummy, while Joe Allen shot straight at Tim Krul.
But Newcastle's threat was clear to see as Hatem Ben Arfa released Ba, but Steven Caulker got back to make a sharp block.
Newcastle were content to sit back on their lead, allowing Swansea to dominate possession, and one extended incisive passing movement ended with Krul beating away a powerful Sigurdsson drive.
Caulker headed over the bar from the resulting corner before Mike Williamson became the first man in the book after a crude challenge from behind on Luke Moore.
Krul held Sigurdsson's long-distance effort from the ensuing free-kick and James Perch blocked another strike from the dangerous Iceland international late in the first half, with Newcastle struggling to get out of their own territory.
Pardew introduced Ryan Taylor at the interval in place of midfield anchor Cheick Tiote and his side came close to conceding an equaliser inside 60 seconds.
Dyer twisted and turned on the edge of the area to again tee up Sigurdsson, whose low shot was deflected just wide of Krul's left-hand post.
Swansea piled the pressure on and Krul was helped by a slice of fortune as Allen's drive flicked off Williamson, struck the keeper and flew away to safety.
Newcastle then lost Ba after the forward appeared to pick up an ankle injury, with Shane Ferguson his replacement.
But the visitors reminded their hosts that they were still a threat as Ben Arfa led a smart breakout that saw Cisse drag an effort just wide of goal.
Needing to find a spark, Rodgers summoned Graham and Sinclair for Dyer and Moore as his side's search for an equaliser intensified.
But, having failed to heed the earlier warning, they fell further behind in the 69th minute as Cabaye again combined with Cisse, with the striker delicately lofting the ball over Vorm into the far corner while off balance.
Swansea's frustration increased as Graham failed to pull the trigger after Sigurdsson had picked the forward out, before the on-loan midfielder could not hit the target from distance.
Rangel then headed wide to sum up their day.