A James Milner penalty, awarded after Gael Clichy's brought down Roberto Firmino, appeared to have put Jurgen Klopp's on course to climb above their rivals.
But Aguero poked home Kevin De Bruyne's cross to snatch a draw, although City are now two points behind Tottenham, who beat Southampton earlier this afternoon.
Christian Eriksen and Dele Alli proved there is life in the north Londoners without Harry Kane as Spurs moved to within 10 points of pacesetters Chelsea.
Kane's absence with an ankle injury meant Son Heung-min led the line but it was Spurs' attacking midfielders who filled the void, with Eriksen breaking the deadlock before Alli won and then converted a penalty.
James Ward-Prowse cut the deficit for Southampton after half-time to spark hopes of a comeback but Tottenham held on.
Chelsea's march towards the title shows no sign of slowing, but victory pulled Mauricio Pochettino's men seven points clear of Manchester United in fifth and nine points ahead of Arsenal, albeit having played a game more than both clubs.
United climbed above the Gunners courtesy of a 3-1 win at Middlesbrough, playing their first game since sacking manager Aitor Karanka.
Ashley Young's deep cross found Marouane Fellaini at the back post to open the scoring, before Jesse Lingard's thunderous strike doubled United's lead after the break.
Boro, with caretaker boss Steve Agnew in charge, did not roll over by any means, though, and when Chris Smalling made a mess of a clearance substitute Rudy Gestede pounced to pull a goal back.
Belief was growing around the Riverside until an embarrassing moment to settled the match as Antonio Valencia capitalised on former United team-mate Victor Valdes' slip to wrap up victory.
Additional reporting by the Press Association