The Manchester City show rolls on. This fifth win of the Premier League season took the tally to 21 goals and added a fourth clean sheet to a formidable start from Pep Guardiola’s men.

It was a duck-shoot as Crystal Palace provided easy prey and their search for a first goal of the campaign continues. They have now lost all six of their opening games and if Roy Hodgson’s side go down next week they will equal Portsmouth’s record of seven straight losses from 2009-10.

The bad news for the Eagles is that Manchester United are up next but City will hardly care about that. What did annoy Guardiola was Neil Swarbrick’s failure to give a penalty after Timothy Fosu-Mensah pulled down the excellent Leroy Sané. However, when Sergio Agüero headed home for the fourth a few seconds afterwards, the smile returned to the Catalan – and his team were not finished.

As Guardiola noted, last year his side won their first six league matches, part of a run of 10 in all competitions. “We have less points than last season,” he said, “but I think we have more goals, conceded less and the feeling is a little bit better. But it’s just September.”

As expected, City were a constant blue swarm throughout. Palace lined up in a 4-5-1 that had Christian Benteke at the tip and Reuben Loftus-Cheek as the midfielder with licence to rove forward. The former Chelsea man came close to an unexpected opener, his shot beating Ederson but going the wrong side of the goalkeeper’s right post. Loftus-Cheek was later guilty of a glaring miss when a run took him deep into City’s area but his radar was awry after Fosu-Mensah picked him out.

Manchester City’s Leroy Sané scores his side’s first goal of the game. Photograph: Nick Potts/PA

As the contest neared the interval, there was some frustration among the home crowd. Now, though, came Sané’s third goal in four days. The German fashioned a wonderful one-two with David Silva that featured a lovely chip from the latter and Sané did the rest with ease. At times it had been attack versus defence, with City completely camped in Palace’s half, so this was just reward for their superiority.

Guardiola made one change from the last league outing and when it was announced it was received as a surprise. Yet after his opener the dropping of the talented Gabriel Jesus for Sané, who scored both goals in the midweek Carabao Cup win at West Brom, seemed smart.

By then City had lost Benjamin Mendy, the French left-back forced off in the 28th minute due to a knee injury, and replaced by Danilo. Following the game Mendy tweeted. “Tough knock for me but i will be ok inch’alla,” he said. Guardiola said he did not know if it was a ligament injury and that more would be known on Sunday.

Hodgson made three changes from his first match in charge, the last of the five previous league losses. Mamadou Sakho started for a first time while Patrick van Aanholt and Luka Milivojevic were also included.

As the second half kicked off, the Silva-Sané combo started up again almost instantly. Another percussive move switched the ball between them and after Sané threatened, Fernandinho was able to shoot but to no avail. Sané, though, was about to turn creator as City moved up the gears.

This was simple and slick: Kevin De Bruyne found Sané down the left and he pinged the ball past Sakho and in to Raheem Sterling and it was 2-0, the winger scoring a fourth goal of the season. Soon afterwards he should have had a fifth. Wayne Hennessey spilled a De Bruyne shot into the lurking Sterling’s path but he hit side-netting not the back of Hennessey’s goal, and Palace escaped.

City’s interplay now was delightful. Agüero went close after an exchange with Silva and Sterling did now strike again. Guardiola has wanted more from Agüero and here he got it, the No10 volleying a neat short-range pass that Sterling rolled home. This was the 22-year-old’s final act. Guardiola paid him a compliment by taking him off on the hour to protect him for Shakhtar Donetsk’s Champions League visit on Tuesday.

By the close it was all so familiar: Fabian Delph added the fifth as Palace became the latest patsies steamrolled by City.

Hodgson, who had seen Benteke limp off in the second half, said: “It is ridiculous to talk about positives after being beaten 5-0, admittedly playing against a top-quality team. We will see some light at the end of the tunnel. I was beginning to see it at half-time, but that light has gone out by the end.”

He may be now be without Benteke due to his injury. “It is a form of ligament damage, but I don’t quite know how bad that is because he is going to have a scan tomorrow,” said the manager.

As for City, they can be expected to improve: it is a frightening prospect.