Newcastle move up to fifth place in the standings. They are three points clear of sixth-placed Chelsea with third-placed Arsenal and Tottenham in fourth - their other leading rivals for Champions League qualification - only two points ahead of them.
Alan Pardew's side scored with their only meaningful attack of the first period on five minutes. Cisse darted onto a delightful pass from Yohan Cabaye to slide the ball beyond home goalkeeper Michel Vorm, who could only get a hand on the shot without diverting the ball wide as it nestled in the net.
His second goal of the day was simply breathtaking as he somehow managed to hoist the ball over Vorm from another Cabaye pass from inside the Swansea area on 69 minutes to ensure the three points docked with his side.
It is the first time since 2006 that Newcastle have managed to win four straight matches in the Premier League.
Swansea dined out on an incredible 80 per cent of possession in the first period without ever looking likely to penetrate the visiting side.
Their best couple of moments in the first period saw Gylfi Sigurdsson drag an effort wide of goal on three minutes with Newcastle goalkeeper Tim Krul forced to swat a Sigurdsson shot over his bar on 27 minutes.
They huffed and puffed in the second half and continued to look pretty without ever looking likely to floor a visiting side who were visibly lifted by Cisse's finishing.
It is the third straight game in which the Senegalese player has come up with a double for Newcastle, who ended the game with their travelling fans chanting the voice of the delighted Pardew.
It is the 13th time a player has scored a double in three successive matches in the Premier League. Cissé is the 12th player to achieve the feat. Alan Shearer is the only player to have accomplished this twice.
The only player in the history of the Premier League who needed fewer than eight matches to find a ninth goal was Coventry City’s Mick Quinn - who needed six matches back in 1992
Since managing to usurp Manchester City a fortnight ago, Swansea have suffered three straight losses in the Premier League for the first time this season. For a newly promoted side who are safe from relegation trouble - they have 39 points and lie 11th in the table - that is quite a stat.
The home team's only problem in this outing was failing to hit the back of the net with some of their passing easy on the eye. Scott Sinclair enjoyed a lively performance when he came off the bench in the second period, but it was not enough to retrieve the situation for Brendan Rodgers's side.
Sigurdsson saw an effort deflect wide of goal early in the second half while Joe Allen saw an effort deflect off Michael Williamson before dropping wide via the frame of Krul, who did well to prevent it from finding his net on 53 minutes.