It was the worst result for the Blues in any competition since their 7-0 Premier League loss to Brian Clough's Nottingham Forest in April 1991 at the City Ground.
Maurizio Sarri's side went 4-0 down in a shocking first 45 minutes at the Etihad Stadium, which led Jamie Carragher to suggest the Italian has turned them into Arsenal since arriving from Napoli last summer.
Second-half efforts from Sergio Aguero – the Argentine completing his 11th Premier League hat-trick to equal Alan Shearer's record – then consigned the Blues to a third defeat in four league games.
The result was Sarri's heaviest ever league defeat as a manager, with the Italian having never conceded more than four before Sunday.
It was also the first time Chelsea conceded four goals or more in consecutive top-flight matches since December 1990 after they lost 4-0 to Bournemouth at the Vitality Stadium on January 30.
Chelsea are now sixth in the Premier League table, a point behind fourth-placed Manchester United who have enjoyed a revival since Ole Gunnar Solskjaer took over in December.
Sarri is under pressure in the Stamford Bridge hot seat and some crucial cup games coming up.
The Blues face Malmo in the first leg of their Europa League last-32 tie on Thursday and then host Manchester United in the fifth round of the FA Cup before the Carabao Cup final against City on February 24.
That fixture at Wembley Stadium in just two weeks time could look particularly daunting after today's heavy defeat.
Chelsea will be hoping January signing Gonzalo Higuain can add to his tally having scored two goals in three league appearances so far, both of which came in the 5-0 win over Huddersfield.
Higuain played all 90 minutes against City but had little service to work with as the visitors enjoyed only 44 per cent possession.