Shelvey took just 87 seconds to open the scoring at the Liberty Stadium with his first goal for Swansea since being sold by Liverpool in pre-season.
The 21-year-old didn't have long to savour the moment of revenge as he produced two careless passes that led directly to Liverpool taking the lead with goals from Daniel Sturridge and Victor Moses before half-time.
But he finished with a smile on his face after providing the assist that brought Michu's equaliser midway through the second half.
Shelvey's evening to remember brought an end to Liverpool's 100 percent start to the season, but the Reds still moved to the top of the Premier League table, one point clear of Arsenal and Tottenham, despite the end of their three-match winning run.
"I just want to say sorry to the Swansea fans for the two bad mistakes that gifted Liverpool a draw," Shelvey told Sky Sports.
"You just want to go into a hole where nobody can see you when you give the ball away for the other team to score, but it has happened to great players over time.
"I showed a bit of character to keep getting on the ball. I still feel I have given Liverpool a draw but it was a great game to play in."
Reds boss Brendan Rodgers added: "Jonjo Shelvey is an outstanding young player, but he knows he has things in his game he needs to improve on.
"He will only do that from playing. Tonight was a steep learning curve for him."
Rodgers allowed Shelvey to leave Liverpool after three inconsistent seasons, so it was clearly a sweet moment when he gave Swansea the lead with less than two minutes played.
After making a hash of an attempted volley from long-range, Shelvey recovered his composure and surged away from Liverpool's new £18 million (21.5 million euros, $28.6 million) centre-back Mamadou Sakho before clipping a fine finish past Simon Mignolet after his first effort was blocked by Martin Skrtel.
It was the first goal Liverpool had conceded in the league this season and Shelvey celebrated wildly.
But within two minutes he was looking to the sky in dismay after his careless mistake gifted Liverpool their equaliser.
Picking up possession just outside his own penalty area, Shelvey flicked a woefully under-hit pass back to goalkeeper Michel Vorm without noticing the lurking Sturridge, who gleefully rifled home a cool left-foot finish.
Sturridge's sixth goal in five matches this season allayed any fears he would be short of sharpness after missing England's World Cup qualifiers against Moldova and Ukraine with a thigh strain.
And Sturridge went close to his second of the night when Vorm brilliantly kept out his header after good work from Moses unhinged the Swansea defence.
Liverpool had made their best start to a campaign since 1994-95 and they took the lead as Shelvey's match took another turn for the worse in the 36th minute.
Under no pressure, the midfielder played a dreadful pass straight to Moses and the punishment was instant.
Breaking from just inside his own half, Moses advanced at pace and, with Swansea's defenders backing off, he unleashed a powerful low shot that left the flat-footed Vorm rooted to the spot.
Liverpool suffered a blow in the second half when Philippe Coutinho was forced off after a bodycheck by Ashley Williams left the Brazilian playmaker visibly wincing in pain.
And their frustrations grew even greater in the 64th minute as Swansea drew level.
Remarkably, Shelvey played a major role yet again as he finally provided an assist for his own team, timing his run to meet a through ball with a clever flicked header into the path of Spanish forward Michu, who slotted past Mignolet for his first league goal of the season.