Michael Laudrup's side had been beaten 1-0 by Valencia in the Europa League and 3-0 by Manchester City in the Premier League in their past two outings but managed to get back on track with a commanding yet lucky display over the Toon who had been on a four-match winning streak.
It took the entire first half for the Swans to open the scoring with Nathan Dyer, who had earlier replaced Alvaro Vazquez, firing home a volley from close range after Magpies keeper Tim Krul could only partially parry Alejandro Pozuelo's leftwing cross.
The win was sealed in the 82nd minute when former Liverpool midfielder Shelvey produced a sublime 25-yard curler to send Swansea up to 11th which saw Newcastle drop to seventh.
Newcastle could have felt aggrieved after the defeat as Swans keeper Michel Vorm was on hand to deny a Loic Remy header while there were penalty calls against Ben Davies for handball and Ashley Williams for a challenge on Yoan Gouffran but referee Howard Webb kept his whistle in his hand.
2013/14 Premier League scores
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