The visitors held on with 10 men in the face of a late onslaught to remain unbeaten in the Premier League and restore their five-point lead at the top of the table
City took the lead through Vincent Kompany in the first half as the captain headed in from a corner, but were quickly pegged back by a Charlie Adam shot which deflected in off Joleon Lescott.
Liverpool were on the front foot for much of the second half, with Joe Hart on top form to deny Luis Suarez, Andy Carroll and others after substitute Mario Balotelli was sent off for picking up two bookings in his 18 minutes on the pitch.
The result means City retain their five-point lead that they came into the weekend with, but could not capitalise on Manchester United's dropped points on Saturday, while Liverpool move up into sixth position in the league.
Craig Bellamy was declared unavailable for the match following the death of his friend and international manager, Gary Speed.
Stewart Downing replaced Bellamy in the team, and manager Kenny Dalglish made one other change to the side who beat Chelsea last weekend as Jordan Henderson came into the team in place of Maxi Rodriguez.
Roberto Mancini made several changes to the team who lost to Napoli in midweek, with Mario Balotelli dropping to the bench along with Pablo Zabaleta.
Gareth Barry returned to the starting line-up, as did Samir Nasri, while Aleksandar Kolarov was left out altogether.
The match started at a frenetic pace in the opening 10 minutes, though little came in the way of true chances.
Yaya Toure came closest to opening the scoring when, following some head tennis in the box after a corner, he fired well over on the half volley.
City looked to be the more likely to open the scoring, keeping a high defensive line and pressing well inside the Liverpool half.
The hosts did look dangerous, however, through the counter-attacking capabilities of Dirk Kuyt, Luis Suarez and Downing.
Kompany was the first player to pick up a booking in the match in the 14th minute, making the rest of his afternoon’s work that much more difficult after a cynical foul on Suarez.
The first real moment of danger came when Jose Enrique attempted a back-pass to Pepe Reina that was seriously lacking in power.
The pass was pounced on by Sergio Aguero, but as he got to the ball he was met with a sliding tackle from Reina. The ball did hit the keeper’s hand, but only after it had rebounded off Aguero, and he could not have done anything to get out of the way.
Aguero was in again after 20 minutes when Charlie Adam was dispossessed by Gareth Barry. Adam was adjudged to have gone down too softly by referee Martin Atkinson.
As City broke, Aguero was turning this way and that, but as he got to the byline he lost his footing and the ball slid out for a goal kick.
While there had not been too much in the way of true efforts on goal, City were having more than their fair share of corners, and one of these led to the opening goal.
It was a fiercely whipped in corner from one of the form players in the Premier League, David Silva.
Kompany beat both of his markers to the ball, and somehow managed to find the back of the net after the ball cannoned of his shoulder and into the far corner.
But it only took Liverpool a matter of seconds to restore the parity. Charlie Adam found himself some way out in plenty of space, and with nothing else really on, he elected for a shot which he had dragged quite badly. It was heading well wide until the intervention of Lescott, who unwittingly deflected the ball past Joe Hart and into the back of the net.
And shortly after the Scotsman really should have put the hosts in the lead after some great play from Suarez put Kuyt through down the left, but the Dutchman was forced wide. After he doubled back, he found the on-rushing Adam just inside the penalty, but he placed his right-footed shot too close to Hart, who managed to save the ball despite heading in the other direction.
The match up until this point had been tense, but was somewhat lacking in intensity and chances, but after the equaliser, the game really seemed to have the potential to become a Premier League classic.
On the stroke of half-time, Aguero forced a save from Reina at his near post, but it was the last action of the half and left the match finely poised for the remaining 45 minutes.
Red mist | Balotelli picked up second yellow card for elbow on Skrtel
The second half began at a very high pace as well, with Nasri slicing a shot wide of the far post after just 15 seconds.
Liverpool took their turn to attack and had penalty shouts turned down after Adam's shot was charged down by Micah Richards, but it was unclear whether the ball did in fact hit the right-back on the arm.
Fifteen minutes into the second half the only thing standing between City and a second goal was Enrique, who did well to cut out Clichy's cross at the back post with Aguero lurking.
Reina had to be on his toes moments later as Aguero looked to get on the end of a through ball. The Spanish keeper misjudged the flight of the ball and was forced to follow Aguero and dive in to tackle, but luckily for him he won the ball.
With three quarters of the game gone, Hart was called into action again, pushing over a Downing volley which had been struck into the ground but was heading into the top corner.
With just over 15 minutes to go, Liverpool came about as close as you can without scoring. Suarez picked up a corner that had drifted over before turning Clichy and firing the ball across from the byline. The ball struck Lescott, and ricocheted onto Kuyt's chest, but this time the defender was in luck as the ball bounced out for a goal kick.
The Reds again came close minutes later as Adam whipped in a devilish free kick that again caused a game of pinball in the box, with the ball bouncing into the thankful arms of Joe Hart. And seconds later Downing shinned a volley across the face of goal with Kuyt agonisingly close to turning the ball in as he slid in at the far post.
The home side were certainly looking the most likely to find a winner as the match drew towards the final stages, with the home crowd willing the ball into the net.
And with the match finely poised as it was, Mancini would have been hoping that his players would keep a cool head. But Balotelli received his marching orders in the 83rd minute, having only been on the pitch for 18 of those. The Italian picked up two quick bookings, one for a needless tug on Glen Johnson, and a second for an elbow to Martin Skrtel's head.
After making such a silly challenge on Johnson only minutes before, the second challenge from Balotelli was careless and he did catch the defender with a leading elbow.
In the closing stages Hart made a good stop from Suarez at his near post before City broke through substitute Edin Dzeko.
Dzeko found an unmarked Silva in the centre, but the Spaniard was tied up by his countryman Reina with Skrtel getting back on the line to clear the eventual shot.
In the last action of the match, Hart was at full stretch to fabulously deny Carroll from a header that surely would have earned the hosts all three points, but the visitors maintained their unbeaten start to the season.
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