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.
Shelvey, though, redeemed himself as he laid on an equaliser for Michu.
Brendan Rodgers had 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.
The midfielder initially scuffed an attempted volley from Jordan Henderson’s poor header, but regained control to ghost pass Sakho and produce a lovely left-footed finish at the second attempt.
But his joy was brief as, still full of adrenaline, he played a blind backpass and failed to spot Sturridge lurking; the striker needed no second invitation.
Shelvey, perhaps understandably, took a few minutes to regain his composure but was guilty of being too eager to make amends, as he scythed down Philippe Coutinho before blazing well over the bar.
Liverpool took a stranglehold on possession and the pace of Moses was proving a real problem for the Swansea defence.
Ben Davies had to block from Henderson after one rangy run from the Nigerian, before he gave Sturridge a simple finish after outfoxing Angel Rangel and Nathan Dyer, but the striker headed straight at Vorm, who deflected the ball wide.
Swansea responded with a lovely exchange of passes between Michu and Wilfried Bony, but the Ivory Coast striker’s shot did not have enough power to trouble Simon Mignolet.
Shelvey then took centre stage again, his risky pass went straight to Moses, who drove at a retreating Swans’ rearguard to beat Vorm.
Swansea could have levelled inside a minute, but Martin Skrtel pulled off a magnificent last-gasp challenge to deny Bony a tap-in after Mignolet had parried a Dyer shot he should have held.
Liverpool almost extended their lead seven minutes into the second half. Swansea were caught sleeping at a free-kick as Henderson crept in at the back post, but Vorm saved from Andre Wisdom after the midfielder had pushed the ball across goal.
Shelvey’s night almost plumbed new depths moments later as he squared up to Lucas after Swansea refused to return the ball after Coutinho limped off with an injury.
But referee Michael Oliver opted to book the pair rather than take more severe action.
And Shelvey’s topsy-turvy evening soon turned on its head once more as he surged forward to cushion a header into the path of Michu, who finished low to Mignolet’s right.
Swansea had renewed vigour and took the game to their visitors during a frantic final quarter, with Jonathan de Guzman forcing a fingertip save from Mignolet, but an engrossing contest ended level.