The Citizens made two changes to the side beaten 3-1 at Monaco, with Yaya Toure and Nicolas Otamendi handed recalls in place of Bacary Sagna and Aleksandar Kolarov.
Jurgen Klopp made one change to the team who beat Burnley 2-1 last time out, with Roberto Firmino preferred in attack to Divock Origi.
Both sides started in a positive fashion, as the rain poured down in Manchester, with the hosts winning a couple of corners which came to nothing.
Twelve minutes in Simon Mignolet had to get down smartly at his near post to keep out a Kevin De Bruyne cross-cum-shot from the left, while a couple of minutes later Sergio Aguero was within inches of turning home a Fernandinho cross.
With 20 minutes on the clock David Silva rifled a shot over the top from 15 yards out when he might have done better, while at the other end Sadio Mane raced clear, only to be thwarted by Willy Caballero.
Philippe Coutinho curled an effort over the crossbar from the edge of the area ten minutes before the break, before Fernandinho somehow shot wide at the far post with the goal at his mercy, after James Milner had seemingly taken out Raheem Sterling who was about to tap home - with referee Michael Oliver surprisingly taking no action.
Home keeper Caballero pushed away a Firmino effort and was called into action again when he tipped over a piledriver from Adam Lallana.
Five minutes into the second half the Reds were handed a penalty, as Geal Clichy was adjudged to have fouled Firmino and Milner calmly sent Caballero the wrong way from the resulting spot-kick.
That setback knocked the Citizens out of their stride a little, although John Stones headed wide from a corner as the hosts did mount a response.
Caballero got a crucial touch to deny Firmino as the Reds hit the home side on a quick counter-attack, while Aguero was unable to direct a header on target from a Silva pass.
However, the Argentinian did much better midway through the second half as he arrived right on cue to sidefoot home the equaliser from a perfect delivery from the right from De Bruyne.
Aguero slipped when through on goal as City pushed for a second goal, with De Bruyne seeing a follow-up hit the outside of the far post.
Lallana then passed up an open goal, as he failed to make contact when Firmino fed him just eight yards out, with the City defence pulled apart.
Aguero sidefooted wide late on and then ballooned the final chance of the game high over the crossbar in stoppage time.