Newcastle had led three times but United pegged them back each time and then won it through Javier Hernandez in the last minute.
That meant they move further clear of City, who lost 1-0 at Sunderland for the second season in a row.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.