Fernandinho's stoppage-time own goal gave Crystal Palace a 2-2 draw at Manchester City, while Wolves fought back from two down to beat Southampton and Norwich City claimed a huge Premier League win on Saturday. (More Football News)
Cenk Tosun's first Palace goal put the London club in front, but Aguero equalised with his 250th for City eight minutes from time before putting the second-placed champions in front at the Etihad Stadium.
Pep Guardiola's side were unable to see it out, though, as Fernandinho turned the ball into his own net to leave City 13 points behind leaders Liverpool, who play Manchester United in one of their two games in hand on Sunday.
Resurgent Saints looked set to move into the top half when they were two up at St Mary's Stadium, but Raul Jimenez's double after a Pedro Neto strike moved Wolves up to sixth.
Norwich striker Teemu Pukki scored the only goal against second-bottom Bournemouth, who had defender Steve Cook sent off for a spectacular save, while fellow strugglers Aston Villa drew 1-1 at Brighton and Hove Albion.
John Fleck rescued a 1-1 draw for Sheffield United at Arsenal, while it was the same scoreline in the clash between David Moyes' West Ham and his former club Everton.
In the final match of the day, Chelsea fell to a shock 1-0 defeat away to Newcastle United.
CITY SLIP UP DESPITE AGUERO BRACE
Palace claimed a stunning 3-2 win at City last season and looked like picking up another three points until Aguero intervened with a late brace.
New boy Tosun headed the Eagles into a first-half lead with his first goal for the club, but the leading overseas scorer in Premier League history levelled to take his City tally to 250 and struck again with time running out.
VAR overturned a penalty decision after Jairo Riedewald was penalised for handball before Aguero equalised and there was more drama when Wilfried Zaha squared the ball, with Fernandinho turning it into his own net.
CHELSEA PAY PRICE FOR MISSED CHANCES
For most of the match at St James' Park, Chelsea were probing and looked the most likely winners.
But despite their dominance of possession, a goal did not arrive with Tammy Abraham the guilty party after squandering two good openings.
Chelsea paid the price four minutes into stoppage time when Isaac Hayden headed in Allan Saint-Maximin's cross.
The loss for Frank Lampard's side means Manchester United have the chance to move within two points of them in fourth if they can find a way to hand Liverpool a first defeat. Newcastle, meanwhile, are 12th with a seven-point cushion over the bottom three.
WOLVES BRING SAINTS BACK DOWN TO EARTH
Saints, on a high after five wins and a draw from their last six games, appeared to be making further strides up the table after Jan Bednarek and Shane Long put them in command at half-time.
But Wolves were transformed after the break, Neto giving them hope and the clinical making Jimenez no mistake from the penalty spot following a VAR intervention for Jack Stephens' challenge on Jonny.
Jimenez was on target again to win in 13 minutes from time, Adama Traore setting the striker up with his second assist, to give Wolves a first win in five in all competitions.
CHERRIES PAY THE PENALTY FOR IMPULSIVE COOK STOP
Norwich claimed their first top-flight win since November courtesy of a Pukki penalty as Bournemouth endured another miserable afternoon at Carrow Road.
Pukki converted from 12 yards 33 minutes in after Cherries defender Steve Cook made an acrobatic one-handed stop to keep out Kenny McLean's goal-bound shot.
Cook was given his matching orders and there was no way back for Bournemouth, who have picked up only four points from their last 12 games, as Norwich held on despite Ben Godfrey's dismissal 13 minutes from time.