James Milner opened the scoring from the spot shortly after half-time, picking out Willy Caballero's bottom-right corner to score his seventh penalty of the season on his Etihad return.
John Stones should have converted a free header as a substandard City tried to improve a dire head-to-head record against Liverpool that had seen them lose five of the previous six meetings between the sides.
Aguero equalised for City with a close-range finish from Kevin De Bruyne's right-wing cross and the Belgian hit the post as Pep Guardiola's side cranked up the pressure in search of a winner.
But it was Adam Lallana who should have scored the decisive goal, the England international somehow mishitting his shot from eight yards after sublime Liverpool build-up play as both teams lost ground on Tottenham in the race for the second – with Manchester United now just four points behind Jurgen Klopp's fourth-placed side.
Simon Mignolet blocked Leroy Sane's cross-shot with his left boot after 19 minutes, David Silva slicing the rebound over the crossbar to spurn City's first real chance of the game.
Penalty appeals were rejected at both ends, with Aguero challenged by Joel Matip as the Argentine tried to connect with Fernandinho's low cross, before Sadio Mane collided with Nicolas Otamendi as he shaped to shoot.
Matip headed Milner's deep free-kick wide after 37 minutes and the game finally exploded into life before the interval.
Milner had to make a brilliant challenge to stop Raheem Sterling from tapping home Silva's cross, with Fernandinho unable to convert at the back post, before Caballero palmed Roberto Firmino's curled shot over his crossbar.
Caballero elected to punch the resulting corner but he could only pick out Lallana, whose powerful volley was beaten away by the goalkeeper.
Chances continued to flow in the second half, with Mane's goal-bound effort deflected over by a Stones block, but Liverpool were awarded a penalty when Clichy clumsily bundled over Firmino.
Former City player Milner tucked away the spot-kick, sending Caballero the wrong way to put the visitors in front, extending City's run without a clean sheet against Liverpool to 13 games.
Stones had a big chance to rapidly respond for City but he headed De Bruyne's corner wide. Caballero then did well to save from Firmino after a superb Philippe Coutinho reverse pass sent his fellow Brazilian into the box.
But after 68 minutes City levelled the scores when Aguero tucked away De Bruyne's cross to continue his record of scoring in all five of his home league games against Liverpool.
COME ON!!!! pic.twitter.com/ujnR7uWFQ9— Manchester City (@ManCity) March 19, 2017
Aguero's one-two with Sane freed the striker for a chance to complete the turnaround but he could not find a finish after losing his balance, De Bruyne slamming the loose ball against the woodwork, then Lallana's opportunity to claim the points arrived.
Emre Can and Firmino combined beautifully to set Lallana up for a golden chance but the midfielder failed to convert and despite a breathless finale - with Aguero unable to turn in Silva's centre and blazing over De Bruyne's chipped cross - the points were shared.
Key Opta stats:
- Manchester City have gone seven consecutive games without defeat in the Premier League (W4 D3 L0); their longest streak in the competition under Pep Guardiola.
- Liverpool have now won more points in 10 games against the top six this season (20) than they have in 10 games against the bottom six (19).
- James Milner now holds the record for the most Premier League games scored in without losing (47 Games: W37 D10 L0).
- Only Gylfi Sigurdsson (11) has made more assists than Kevin De Bruyne (10) in the Premier League this season. The Belgian has assisted Aguero more times than any other player this term (3).