The Slovakian gave the hosts a deserved lead in the first half, but a lapse in concentration allowed the Argentine striker to earn his side a point with his 100th goal in England
The defender had given his side a half-time lead before Yaya Toure equalised just past the hour mark, before a Luis Suarez free-kick looked to have earned the Reds victory until Skrtel's error allowed Carlos Tevez to score his 100th goal in English top-flight football.
Brendan Rodgers handed a Premier League debut to 17-year-old Raheem Sterling after he impressed during midweek against Hearts, with Luis Suarez and Fabio Borini joining him in a three-pronged attack as Lucas returned to domestic action at Anfield after his lengthy lay-off.
The champions elected for a 5-3-2 formation, with Mario Balotelli replacing the injured Sergio Aguero alongside Carlos Tevez up front. David Silva, meanwhile, was dropped to the bench.
The match began at a decent tempo, with the hosts looking to bounce back from their worst opening-day defeat in over 30 years in the top flight, while City were hoping to continue their winning ways.
Sterling was lively from the start and almost gave Liverpool an early lead as he crossed from the left for Borini, but the Italian could only prod his volleyed effort narrowly wide of Joe Hart’s left-hand post.
The hosts’ bright start was spoiled somewhat as Lucas limped off with just four minutes on the clock, with an injury believed to have been sustained during the pre-match warm-up.
The Argentine was played in behind Martin Skrtel by a clever pass from Samir Nasri, and he skipped away from Pepe Reina before cutting the ball back from a tight angle only to see it bounce agonisingly across the goal line and off the far post, allowing Martin Kelly to clear.
Roberto Mancini was visibly furious that no City players had gambled on a potential rebound, and just after the half-hour mark, his side were punished for their profligacy in front of goal.
Steven Gerrard’s fierce cross from the right was blocked just over the bar by Vincent Kompany, much to the relief of Hart. From the ensuing delivery, however, Skrtel was allowed to travel ten yards without pressure from the City defence to power an unstoppable header past England’s no.1 and send the watching Kop into raptures.
City tried to rally but they were harried and harassed all over the pitch, with the Reds’ work-rate making them look a completely different side to the one that limped to a 3-0 defeat to West Brom last weekend.
Nasri had half a chance when he tried his luck following Kolarov’s blocked free-kick, but the Frenchman was closed down quickly on the edge of the area and the referee drew a breathless half of football to a close.
The second half began in much the same way that the first finished, with Liverpool keeping the tempo high and frustrating City’s midfielders by denying them time on the ball.
Rodgers’ side carved out the first meaningful chance when Borini capitalised on a sloppy pass from Kolarov and found Suarez in the box, but the Uruguayan could only scuff his effort wide under pressure from Kompany.
The champions, so often dominant in the middle of the park, were struggling to cope against the pressure from Liverpool’s central players and Mancini moved to alter the flow of play on the hour mark as Nasri was replaced by former Evertonian Jack Rodwell.
Moments later, the disappointing Balotelli was withdrawn for Edin Dzeko, as City looked for a way past a resolute home defence – and with 63 minutes on the clock, they did just that, in somewhat fortuitous style.
Tevez did well to find space on the right hand side of the area. He clipped the ball towards the far post where Reina came and failed to claim it, before the ball bounced off the standing leg of Kelly to allow Yaya Toure a simple finish.
Liverpool would have felt hard done by to surrender their lead in such a sloppy manner, but less than five minutes later, they regained their advantage in sumptuous style.
Gerrard won a free-kick 25 yards from goal, and Suarez stepped up to bend a stunning shot round the wall and into the bottom corner, beyond the despairing dive of Hart.
Mancini’s men pressed for an equaliser once more and brought David Silva on for the final fifteen minutes, but it was Liverpool who looked consistently the more likely to score as they continued to boss possession and cause the visitors problems down the flanks.
The champions had been frustrated for long periods by a resolute Liverpool defence, but with ten minutes to go and with his side in total control, Skrtel handed City a way back into the match.
The Slovakian played a needless backpass without looking straight to Tevez, who rounded Reina and slotted home his 100th goal in English football to silence the home crowd.
Liverpool recovered and almost got back into the lead just two minutes later when JonJo Shelvey fizzed a left-footed drive over the bar, before Dzeko dragged an effort a couple of feet wide of the left-hand post.
The hosts threw on Andy Carroll to see if he could replicate his goalscoring heroics against City from two years ago, but Dzeko almost broke the deadlock before the England man had touched the ball, firing left-footed over the bar from six yards after Kolarov’s cross from the left.
Carroll then came close to finding the back of the net after Suarez looped the ball back across goal following a corner, but Rodwell was well placed to nod the ball off the line.
The match ended in suitably hectic style as both sides went all-out for three points, but despite late efforts from Glen Johnson and Tevez, neither team had enough to edge what was a terrific game of football.