Jamie Vardy, having been dropped from the starting lineup, was summoned from the bench only to miss the spot kick with his first touch.
"We are there, we are the leaders, but Liverpool have one more game (in hand)".
Chelsea on the other hand slip to sixth with the scale of the defeat sure to raise further doubts over Sarri's future.
It was Chelsea's third consecutive away loss in the league, following a 2-0 collapse at Arsenal and 4-0 humiliation against Bournemouth.
And this was their worst loss in any competition since 1991 after failing to recover from Sterling's fourth-minute opener. With a cleverly taken free kick down the right, Kevin De Bruyne released Bernardo Silva, who cut back for Sterling to strike into the net.
Pep Guardiola is delighted with what has been a hugely profitable week for Manchester City with big wins over Arsenal, Everton and Chelsea.
Aguero should have doubled the lead nearly immediately but remarkably missed from two yards.
To show how things have turned around, United now have a better goal difference than Chelsea, having been 21 goals worse off before Solskjaer's first game against Cardiff on December 22.
Sterling's pace and skill drew a clumsy Cesar Azpilicueta foul inside the box and Aguero beat Kepa once more with an excellent penalty.
City eased off for the remainder of the first half, and Gonzalo Higuain even managed to test Ederson with a sharp volley, but the hosts clicked back into gear after the break.
But Chelsea do not show much patience with failing managers and the current incumbent was skating on thin ice before his team were dismantled by City. Jurgen Klopp's side must respond in their next league game, which happens to be against United at Old Trafford in two weeks.
The record had been held by Eric Brook since1940, who had 158 goals to his name, but the Argentine equaled and then broke that record in an incredible attacking display at the Etihad Stadium.
This gritty success was the ideal preparation for hosting Borussia Dortmund in the Champions League last 16 first leg on Wednesday.
You can view all of the best pictures from the win via the gallery below!
Asked if it was one of City's best performances of his reign, Guardiola said: "Yes, we played good".
Indeed, the Blues have lost five times in the last two months to leave their hopes of finishing in the top four in doubt.
"I don't know", Sarri said.
"I told him not to do it again but, after, his reaction was a little bit better!"