Shelvey scored the first after just two minutes before twice giving the ball away for Daniel Sturridge and Victor Moses to score and put Liverpool ahead at the break.
However, the midfielder atoned for his earlier errors, heading into the path of Michu to equalise after 63 minutes as Liverpool dropped points for the first time this season.
Brendan Rodgers handed debuts to two of his deadline-day acquisitions, with Mamadou Sakho and Moses both making their Liverpool bows.
For Swansea, Leon Britton and Nathan Dyer replaced Jose Canas and Pablo Hernandez.
Shelvey opened his account for the Welsh club early on as his former employers conceded for the first time in the league this term.
The 21-year-old miscued a volley from the edge of the area but picked up the loose ball, evaded a challenge in the box and steered a calm finish past Simon Mignolet.
However, Shelvey's night took a turn for the worse two minutes later as his loose backpass towards Michel Vorm found Sturridge.
August's player of the month made no mistake as he pounced to equalise and, in the process, become the first player to score in each of Liverpool's first four games of a Premier League season.
After the two early goals, chances were few and far between thereafter until the 25th minute, when Moses dug out a cross from the left wing for Sturridge, who forced a scrambled save from Vorm with his close-range header.
Michu and Wilfried Bony linked well for Swansea just short of the half-hour mark, only for the Ivorian to shoot tamely at Mignolet.
But Liverpool went ahead eight minutes before the break as Moses seized on another sloppy pass from Shelvey to race through and fire past Vorm.
Bony almost levelled after Mignolet parried Dyer's save shortly after but Martin Skrtel's block proved crucial as he kept his side ahead.
Andre Wisdom brought a good save from Vorm seven minutes into the second half, after the Dutchman had parried a Jordan Henderson effort.
Shelvey's eventful night continued three minutes after the hour when he neatly nodded the ball into Michu's path for the Spaniard to level the scores from close range.
Jonathan de Guzman saw a late free-kick tipped wide by Mignolet as Swansea finished the game on top without finding a winner.
The hosts climb to 13th, while Liverpool edge ahead of Arsenal and Tottenham at the summit.
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