Shelvey scored Swansea's first goal and created their second but two shocking passes set up both goals for Liverpool, who moved a point clear of Arsenal and Tottenham Hotspur at the top of the table.
Shelvey, who joined Swansea for 5 million pounds from Liverpool in July, gave his new team the lead after two minutes when he swept a shot into the net at the second attempt from six metres.
But two minutes later a weak back pass was pounced on by Daniel Sturridge, who fired the ball past goalkeeper Michel Vorm for his fourth goal in four games this season.
Another loose pass by Shelvey after 36 minutes was easily picked off by Victor Moses and the winger, on-loan from Chelsea, broke forward and slotted the ball past Vorm from the edge of the area.
Shelvey's deft header set up striker Michu for Swansea's equaliser after 64 minutes and the home side, 13th in the standings with four points from four games, looked more likely to snatch a winner in the closing stages.
