“Vinci Per Luca” read a banner draped over the Chelsea end. Win for Luca was the request but Graham Potter’s outclassed team were unable to deliver as Manchester City cruised into round four. The teams have met three times in three different competitions this season, City victorious and shutting out Chelsea every time.

To compound the misery for Potter and the Chelsea co-owner Todd Boehly, the names of the former manager Thomas Tuchel and former owner Roman Abramovich echoed from the away section as their expensive, ineffective side slipped to another defeat.

Chelsea’s first third-round exit for 25 years – when the late Gianluca Vialli scored twice in a 5-3 defeat against Manchester United – continued their miserable run of form and results under Potter. It is now five defeats in seven games for the former Brighton manager and five games without a goal in that sequence. They never troubled City’s stand-in goalkeeper Stefan Ortega throughout a chastening cup tie. City operated on a different level, scoring three in the first half through Riyad Mahrez, Julian Álvarez and Phil Foden.

The excellent Mahrez added a fourth from the penalty spot late on. Both clubs paid a fitting tribute before kick-off to Vialli, who died on Friday aged 58 and whose name was chanted regularly by the 8,000 travelling supporters. Chelsea players warmed up in No 9 shirts in memory of their former player and manager while the entire stadium rose to applaud the great Italian when his picture appeared on the giant screens.

City then got on with the business of ushering Chelsea out of another cup in an utterly dominant first-half display. Guardiola made seven changes from the win at Stamford Bridge on Thursday, Potter six, with the teenagers Bashir Humphreys and Lewis Hall starting in the visitors’ defence, the new signings Benoit Badiashile and David Fofana on the bench and Pierre-Emerick Aubameyang joining a lengthy injury list with a bad back.

The Chelsea manager’s plan was to contain and strike on the counterattack but neither was executed convincingly as his team were gradually taken apart. There were boos from the away end when the half-time whistle sounded and many fans did not return for the second half.

A double substitution at the break suggested Potter had a similar opinion on Chelsea’s opening 45 minutes. It was a cagey start with City probing patiently against an initially compact visiting side. The lively Cole Palmer squandered the first chance when played through by Aymeric Laporte’s lofted pass. Palmer had the World Cup winner Álvarez unmarked to his right but opted to shoot through the legs of Kepa Arrizabalaga and struck the side-netting. There would be no cause to rue the miss.

The hosts took the lead five minutes later courtesy of a stunning free-kick from Mahrez. The match-winner on Thursday was fouled 25 yards out by Hall and brushed himself down to curl an unstoppable free-kick into Arrizabalaga’s top left-hand corner. The shot may have taken a touch off the Chelsea wall but that did not alter the flight of the ball as it flew beyond the Chelsea keeper, giving Mahrez his third goal against the Stamford Bridge club this season.

City were soon handed a second. Literally. Play continued after Chelsea cleared a corner from Palmer but referee Robert Jones was instructed to check his pitchside monitor by VAR. There he spotted an inexplicable handball by Kai Havertz, who had been fortunate early on not to be penalised for standing on Rodri’s foot, as he challenged with Laporte for a header at the corner. Jones pointed to the spot and Álvarez, making his first start since the World Cup, drove the penalty into the bottom corner. Arrizabalaga got a hand to the spot-kick but could only turn it on to the post and in.

The third was peak City, a sublime team goal that killed the tie, encapsulated the fun their players were having and sent some Chelsea supporters to the exits. Sérgio Gómez and Álvarez worked the ball to Rodri on the left and he switched play with a glorious cross-field pass on to the toes of Mahrez. The winger fed Kyle Walker as the right-back motored into the penalty area and, when he cut the ball back fron the by-line, Foden stretched to steer a finish past Arrizabalaga.

It was almost four before half-time with Álvarez inches away from converting Mahrez’s low cross along the face of Chelsea’s goal. Potter replaced Havertz and Mateo Kovacic with Fofana and Denis Zakaria respectively for the second half.

There was modest improvement in the Chelsea performance but never enough to threaten even a consolation goal. Police and stewards moved in to the away section in the second half to remove Chelsea fans who had been throwing drinks and objects on to City supporters in the tier below. Those that remained for the closing stages saw Mahrez make it four from the penalty spot after Foden had been clumsily upended by Kalidou Koulibaly. Oxford or Arsenal await City at the Etihad Stadium in round four. Another inquest awaits Potter.