It was the fifth time in six league games in which Pep Guardiola's side have struck inside the opening 20 minutes, a sequence that includes two first-minute goals.
For Sarri, it was the heaviest defeat of his coaching career and raised questions over his future.
And this was their worst loss in any competition since 1991 after failing to recover from Sterling's fourth-minute opener. Kevin De Bruyne released Bernardo Silva down the right with a cleverly-taken free-kick and the Portuguese cut back for Sterling to smash home.
Chelsea lost Sarri's first game in charge, August's Community Shield with Manchester City, before embarking on an 18-match unbeaten run.
Guardiola fell to the floor in exasperation when Aguero somehow side-footed wide with his easiest chance of the game moments later. "He just proves week after week how good he is, year after year".
While the Portuguese ultimately failed at Manchester United, things haven't exactly improved much at Chelsea.
4 - Chelsea have shipped a minimum of four goals in consecutive away league games for the first time since December 1990.
To make matters worse for Jorginho, both Mateo Kovacic and Antonio Rudiger were further away when they charged back towards Chelsea's goal and ended up overtaking their Chelsea teammate.
At Wembley, the win put Spurs five points off the top of the table as they try to catch pace-setters Liverpool and Manchester City.
An under-pressure Sarri must now rouse his players for Thursday's Europa League knockout tie with Swedish side Malmo.
"I don't know, you have to ask the club", said Sarri, who was hired after leaving Napoli.
The Russian has been absent from games this season, and Sarri revealed after the chastening defeat to City that he "never" speaks to his boss.
All four goals conceded at Bournemouth came in a second-half collapse, while City hit four inside the first 25 minutes at the Etihad.
"I would think that when you think what [Kante] did previous year, he was head and shoulders ahead of anyone else", Harris said.