The Citizens took the lead in the 43rd minute at Old Trafford when David Silva bundled home from close range.
Manchester United, though, drew level before half-time when Marcus Rashford slotted home to make it 1-1 at the break.
However, Manchester City claimed all three points when Nicolas Otamendi hit home the eventual winner shortly after half-time following Romelu Lukaku’s failed clearance.
Manchester City enjoyed large spells of possession as the notched up their 14th win in a row in the Premier League.
And former Manchester United defender Neville had no choice but to concede that Manchester City were by far the better team on Sunday afternoon.
Speaking to Sky Sports after the game, Neville said: “I thought City were a different level to Man United.
“In the second half, United didn’t have the quality. It’s tough to do what they’ve done today. To dominate the game and show authority and confidence… Not many teams do that [at Old Trafford].
“I even saw some Man United fans clapping City off.”
Manchester United, who are now 11 points behind their bitter rivals, will look to return to winning ways when they take on Bournemouth at Old Trafford on Wednesday night in the Premier League.
The Red Devils have not won the Premier League title since their famous final triumph under Sir Alex Ferguson back in 2013.
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