Shelvey, who left the Reds for south Wales in the summer, fired the Swans into the lead after just 87 seconds.
However, two terrible errors from the midfielder allowed the in-form Daniel Sturridge and Liverpool debutant Victor Moses to put the visitors ahead.
However, Shelvey redeemed himself as he laid on an equaliser for Michu.
Brendan Rodgers has brought the Merseysiders to his former club with three wins from three on the board, but they were given a rude awakening when Shelvey rounded £18million signing Mamadou Sakho with ease before curling left-footed into the net.
The England international initially celebrated with gusto but reined himself in in front of the away end.
But he had few reasons to smile just 99 seconds later as a horrible backpass ended with Sturridge scoring his 12th goal in 10 games.
He then compounded the mistake by hitting a pass straight to Moses, who raced away to steer beyond Michel Vorm.
But, with his temper beginning to fray, Shelvey's clever header set Michu up for his first league goal of the season to cap a remarkable night for the former Charlton man.
So much of the build-up had centred on Shelvey's first meeting with his former employers, and he made a dream start.
Source: PA
Source: PA