The ex-Reds midfielder got his new club off to a flyer on two minutes when he latched onto a rebound and curled a fierce shot beyond Simon Mignolet from eight yards.
But Shelvey's dream start turned into a nightmare just over 60 seconds later when he gift-wrapped a back pass straight to Daniel Sturridge, who made no mistake with a clinical strike into the bottom corner.
And it got even worse for the Swans playmaker on 36 minutes when his attempted cross-field pass landed straight at the feet of Victor Moses. The on-loan Chelsea man seized on the opportunity and raced at goal before lashing in a low shot to mark his debut in style.
Liverpool looked on course to stretch their winning start to four matches but were forced to settle for a point when the Swans grabbed a deserved equaliser just past the hour.
Once again Shelvey was at the heart of the goal, nodding a clever ball into the path of Michu who ensured the Jacks moved out of the relegation zone with a crisp low finish.
Shelvey later apologised to the Swansea fans for his errors. He said: "I just want to say sorry to the Swansea fans for the two bad mistakes that gifted Liverpool a draw and I thought we deserved more than that."
2’ GOAL – 1-0. Shelvey comes back to haunt Liverpool with the opener! The midfielder miscues a shot from 25 yards and then shimmies past Sakho before seeing his effort blocked by Skrtel. But the ex-Red is first to the rebound and curls a shot beyond Mignolet to get the Jacks off to a flyer.
4’ GOAL – 1-1. Sturridge takes advantage of a huge error by Shelvey to drill a low shot into the corner. From hero to villain for the ex-Reds midfielder in the space of 60 seconds.
25' GREAT SAVE - Moses weaves beyond two defenders on the left and clips in a delightful cross for Sturridge who guides his header down, only to be brilliantly denied by Vorm.
36' GOAL - 2-1. Shelvey has another nightmare as his raking pass is easily picked up by Moses, who races at goal before driving a low shot in at the near post from 20 yards. Not a bad way to mark his debut.
64' GOAL - 2-2. Michu latches onto Shelvey's clever knock down and stabs the ball beyond Mignolet. The night suddenly looks a bit brighter for Shelvey. A goal, two glaring errors and now... an assist.
88' GREAT SAVE - De Guzman curls a delightful free-kick towards the far corner but Mignolet is there to push it to safety. The Reds keeper has had a great start to life at Anfield and could well have earned his side a point to go back to the top of the table.
Sturridge becomes the first ever Liverpool player to score in the first four games of a Premier League campaign.
Liverpool miss out on the chance to win their first four Premier League matches for the first time in their history. The last time the Reds were 100 per cent after four games of a league season was in 1990-91.
Brendan Rodgers' side have now lost just once in 16 league matches.
Since winning the League Cup back in February the Swans have won just three of their last 15 league games.
TALKING POINT - One man: Jonjo Shelvey. The former Liverpool midfielder endured a night of mixed fortunes. The youngster got his new club off to a flyer with some fine perseverance for the opening goal. But it all turned sour when he gifted both Sturridge and Moses possession in dangerous areas, leading to Liverpool's two goals. He made amends by teeing up the equaliser for Michu and was quick to apologise to the Swansea fans for his mistakes in his post-match interview.
MAN OF THE MATCH - Daniel Sturridge (Liverpool): The England striker just can't stop scoring at the moment and was a real menace, particularly in the first half. Unlucky not to double his tally with a header that was well saved.
PLAYER RATINGS -
SWANSEA: Vorm 6, Rangel 6, Chico Flores 8, Williams 6, Davies 6, Britton 6, Shelvey 6, Michu 8, Dyer 6, Routledge 6, Bony 7. Subs: de Guzman 7, Pozuelo 5.
LIVERPOOL: Mignolet 8, Wisdom 6, Skrtel 7, Sakho 6, Enrique 6, Lucas 6, Gerrard 7, Henderson 6, Coutinho 6, Moses 7, Sturridge 8. Subs: Aspas 6, Toure 6, Sterling 6.