Pep Guardiola's side delivered the perfect response to last weekend's first league loss of the season at Liverpool by overcoming the stubborn challenge of Rafa Benitez's side to go 12 points clear at the top of table.
Kun then bagged a second-half penalty and after the Magpies had narrowed the defict through Jacob Murphy's breakaway goal, Sergio sealed the points by rifling home after some sensational skills by Leroy Sané for the 11th hat-trick of his City career.
"We're really happy with the victory - we needed it after last week," said Sergio.
"It's a long season though and we've not won anything yet. We need to keep going and pushing onto the next game."
And when pressed as to whether the opening goal was his or went in directly from De Bruyne's brilliant cross, Sergio added: "Of course it was my goal - I think it touched my hair. It’s mine, sure, 100%!"
Kun's team-mate Oleksandr Zinchencko hailed the impact of the City strike legend, who maintained his incredible goal-scoring record against the Magpies.
And the young Ukranian, who produced a fine display on what his first start in the Premier League, was in no doubt as to Kun's importance to the club.
"I'm very happy for Sergio, he's a life legend. When it was 2-1 it was a little bit dangerous but we scored more," said Oleksandr.
"I'm so happy (to make my first start in the Premier League) and it's an important three points after Liverpool, we have to keep going."