The Argentinian doubled City’s lead over Chelsea early in the first-half, scoring a wonderful curled effort past Ederson, before making it 3-0 before the 20th minute.
But just minutes earlier, Aguero missed the simplest of chances from just a few yards out.
After twisting and turning in the box, Bernardo Silva managed to somehow square the ball for his City team-mate, who simply had to tap home into an empty net.
But City fans couldn’t believe it when Aguero sent the ball into the side-netting – and neither could Guardiola.
As a Sky Sports camera panned to him, the Spaniard put his hands over his face, pulled his hood over his head and fell to the ground, with his face planted on the Etihad turf.
Guardiola was soon back on his feet and got the chance to celebrate two Aguero goals in the next couple of minutes.
Speaking about Aguero before the clash, the City boss said: “It is what it is. The big players need to be there in the big moments and he did it, time and time again.
“Hopefully he can continue. The game belongs to the players. The big games belong to special players.
“That is what he is about. When the best tennis players need to save a break, they serve an ace.
“Big clubs need this kind of player.”
City can move level on points with Liverpool should they win this afternoon.
The Reds returned to the top of the Premier League by beating Bournemouth on Saturday.