Manchester City will fly to Basel for Tuesday’s Champions League last-16 match in fine heart after this impressive win. Their lead at the top of the Premier League is 16 points – although Manchester United play on Sunday – and they need a maximum 21 more for a third Premier League title in six years.

“My advice for the players is not to think how many games are left, just to look to the next one,” Pep Guardiola said. “If we are able to win the title it will be something special.”

Sergio Agüero gave the latest illustration of his excellence with a second hat-trick in three home games and ended with his count for the club at 197. His third came on 77 minutes and was the result of a Kasper Schmeichel mistake that ceded the ball to him. Agüero calmly chipped the Leicester No 1 to make it 4-1 to end the contest before he smashed in a fourth at the close.

It left his manager purring. “Sergio has an amazing talent in the box,” Guardiola said. “So we try to create a lot of chances to score, and he always does. Congratulations to him because it’s not easy to score four goals.”

The City manager made two changes after the draw against Burnley last weekend, dropping Danilo and Vincent Kompany to the bench for Oleksandr Zinchenko and Aymeric Laporte. Claude Puel decided Ben Chilwell and Matty James should start for Leicester and that Danny Simpson and Kelechi Iheanacho should be substitutes. Riyad Mahrez’s exile ended, with the Algerian taking a place on the bench against the team who tried to buy him late last month.

Manchester City have only lost once at home under Guardiola and what any opposition do not need is to concede early. But after 125 seconds Leicester did exactly that. This, inevitably, was created by the sublime Kevin De Bruyne. The Belgian sliced the ball behind a stricken defence and there was Raheem Sterling to poach his 20th goal of the season.

Guardiola marvels at Manchester City points total – video

From here Guardiola’s side performed lightning-quick play that is almost impossible to defend against. One move had the ball relayed from Sterling to Ilkay Gündogan through to Agüero and suddenly he was clear though but could not finish.

Now, Leicester gave a warning with their own quick break, the ball pinging between Christian Fuchs, Fousseni Diabaté and Jamie Vardy. After Agüero again dallied at the end of Manchester City’s next break, Leicester equalised.

It stemmed from a howler by Nicolas Otamendi, the occasionally suspect centre-back misplacing a pass straight to Vardy. After Zinchenko and Gündogan each tried and failed to tackle, the centre-forward raced in on Ederson’s goal and beat him with a sweet right-foot finish for a 14th league strike and four in four outings.

City’s draw at Burnley was a rare recurrence of one of last season’s main issues for Guardiola’s side: profligacy in front of goal. Until the second-half goal glut, there were signs the problem might cost City more points. Kyle Walker took up an excellent position for a cross but spooned it over his team-mates. Then De Bruyne found Sterling and he rounded Schmeichel but hit Aleksandar Dragovic’s flailing leg.

Normal finishing service was resumed three minutes into the second half. Yet again it was De Bruyne who made Agüero’s goal after Sterling passed to him. De Bruyne’s speed of thought and execution is always a fraction ahead of the game and the way he found Agüero from a running, sideways-on position was superb. It handed the striker a simple finish and his 25th goal of the season.

The 26th came moments later and yet again De Bruyne was provider for a 14th league assist, the competition’s highest. His pass found Agüero who did the business, though Schmeichel will be disappointed the finish went under his body.

On 62 minutes Puel made a decision. On came Mahrez and Iheanacho for Diabaté and Chilwell. It was a positive move but Agüero killed the match in his signature style to make it 13 in his last 10 appearances.

Of Mahrez’s cameo, Puel said: “He made perhaps a mistake. The most important thing is he came back to the training session, to the game.

“Now it’s important to look forward, and put this behind us, with the next games coming up. He’s a valuable player for this team, like Vardy. The other players welcomed Riyad and that’s a good thing.”