The Swans begun the campaign brightly but fell away after some impressive performances and on paper it appeared as though that trend would continue but the Magpies have not been at their best lately and were unable to capitalise to fall at home for the second time in two games.
Michu grabbed his seventh goal of the campaign in the 58th minute when he headed home Pablo Hernandez's cross before Jonathan de Guzman added a second three minutes from time with a tight finish after Toon keeper Tim Krul had denied Danny Graham.
That preceded a consolation goal for Alan Pardew's side with Demba Ba making it 2-1 in the final minute with a header of his own but the Senegalese striker was wasteful early with a number of gilt-edged chances going begging.
Swans gloveman Gerhard Tremmel produced a number of fine saves to deny Newcastle, especially Hatem Ben Arfa's golden opportunity in the first half, and in the end Michael Laudrup and his Swans walked away from the Northeast with maximum points.
The victory allowed Swansea to move up to 10th on the table as Newcastle fell to 12th as they have won just once in their past seven.
Sports Direct Arena, Newcastle-upon-Tyne - 49,403