Rodgers had sold midfielder Jonjo Shelvey to his former side just a few weeks earlier, and the England international made an immediate impact as he lined up against his old team, opening the scoring just 87 seconds into the match, curling the ball in from a tight angle after rounding summer signing Mamadou Sakho.
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Shelvey was hero-turned-villain down the other end just a few moments later, though, as a careless back-pass set up Daniel Sturridge to get the visitors back on level terms, netting his 12th goal in 10 appearances.
Shelvey had a role to play in Liverpool's second goal of the night later in the first half too as he gave away the ball in midfield to Victor Moses, who was on loan with the Reds from Chelsea for the 2013-14 campaign. The Nigeria international quickly ran towards the Swansea goal, rounding Chico Flores before dodging a last-gasp challenge from Shelvey as he tried to make amends for his error, leaving Moses to rifle the ball into the bottom corner.
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Simon Mignolet came under pressure before half time as the home side tried to get back on level terms again, but he parried an effort from Nathan Dyer before stopping Wilfried Bony's follow-up, ensuring that Liverpool were in front at the interval.
It was Michel Vorm who was the busier of the two keepers early in the second half, as Andre Wisdom and Jordan Henderson both attempted to extend the visitors' advantage, but the Dutchman kept Swansea in contention.
After an eventful first half, it was Shelvey who was involved again just after the hour mark as he nodded the ball past Martin Skrtel, setting up Michu for a first-time strike into the back of the net, getting the home side back on level terms for the second time.
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Jonathan de Guzman came closest to grabbing a winner late on when he attempted to curl the ball in from a free kick, but Mignolet tipped his finish behind to ensure that both sides finished with a point.
The draw left Swansea 12th in the table having won just one of their opening four matches of the season. A win in their next outing lifted them up to ninth, but they would not get any higher during the season, and a poor run of form after New Year cost Michael Laudrup his job, eventually resulting in Garry Monk's appointment.
For Liverpool, a point was enough to keep them at the top of the standings, despite dropping points for the first time in the season. However, they were beaten to the title by Manchester City, winning just one of their final three matches of the campaign.
Since this match, Michu has scored just one more goal in the Premier League for Swansea, finding the back of the net in their 2-0 win over Crystal Palace just six days later. The Spaniard spent last season on loan with Napoli, and has not featured for Monk's side this season, having been told that he was free to leave during the summer transfer window.
Rodgers has won all four of his matches against his old side since, including their most recent meeting at the Liberty Stadium in March, which saw the visitors come away with a 1-0 victory. They meet for the first time in the 2015-16 season in November at Anfield.