Three of the champions' goals in a one-sided encounter at the Etihad Stadium came in a 15-minute spell late in the first half as Mahrez, Julian Alvarez - from the penalty spot - and Phil Foden all found the target.
Mahrez added a fourth with City's second penalty of the afternoon five minutes from time.
It was City's second win over the out-of-form Londoners in the space of four days and piled on the frustration for their manager Graham Potter.
After a run of just one win in seven in all competitions, Chelsea supporters booed their side and were also heard chanting the names of former owner Roman Abramovich and ex-manager Thomas Tuchel.
City have no such concerns and, as well as looking to reel Arsenal in at the top of the Premier League, could now be hosting them in the fourth round - if the Gunners can see off Oxford on Monday.
City, who rested Erling Haaland and Kevin De Bruyne, effectively had the game wrapped up by half-time.
The sides made 13 changes between them from the teams that played each other on Thursday but it was soon apparent City boasted greater strength in depth.
Chances were scarce as the game began at a slow tempo but City comfortably established control.
Mahrez first threatened when he beat Lewis Hall on the right but Kepa Arrizabalaga claimed his cross.
Cole Palmer wasted a golden opportunity after 13 minutes when he latched onto a long ball from Aymeric Laporte and shot into the side-netting instead of squaring for Alvarez.
Mahrez made no mistake, however, after he was fouled just outside the area by Hall. He got up to curl a superb free-kick into the top corner, albeit via a slight deflection off the wall, to put City ahead after 23 minutes.
Things got worse for Chelsea on the half-hour when Kai Havertz inexplicably charged and punched the ball away defending a corner. The offence was initially missed by referee Robert Jones but there was no escape for Havertz following a VAR review.
Alvarez fired the resulting penalty past Kepa despite the keeper getting a hand to his shot and having done his best to put the World Cup winner off with some words as he placed the ball on the spot.
Alvarez went close to another soon after but Kalidou Koulibaly just did enough to take the sting out of his effort.
Foden made it 3-0 when he rounded off a fine team move seven minutes before the interval.
The ball was spread from the right to the left and then back to the right, where Mahrez controlled brilliantly and casually fed the onrushing Kyle Walker to cutback for Foden to tuck home.
City went close again on the stroke of half-time when Alvarez was inches away from connecting with a Mahrez cross.
Such were Chelsea's struggles, they did not even register a shot until a Mason Mount effort was deflected wide in the 55th minute.
City eased off but Mahrez curled an effort narrowly wide in the 73rd minute. He then did even better from the spot late on after Koulibaly bundled over Foden.