The Premier League leaders beat the Magpies 3-1 thanks to a Sergio Aguero hat-trick on Saturday after they succumbed to their first Premier League defeat of the season at Liverpool a week prior.
United had briefly cut the gap to nine points after Anthony Martial's strike gave them a 1-0 win at Burnley earlier in the afternoon, but City remain relentless in their pursuit of the title with Aguero netting the opener on 34 minutes, adding a penalty on 63 before finishing off a lovely move prompted by Leroy Sane on 83 minutes.
The deadlock was finally broken when Aguero met Kevin De Bruyne's fierce cross with a glancing header into the bottom corner of Karl Darlow's goal. Jacob Murphy pulled one back for Newcastle after a mistake by Nicolas Otamendi but Aguero had the final say in the 83rd with a fine turn and shot.
After losing 4-3 against Liverpool the previous weekend, this Etihad Stadium contest was always likely to ask questions of City's squad and their ability to return to winning ways after the Anfield defeat ended their remarkable unbeaten start to the season.
Promoted Brighton have picked up just two points from their last four games and are three points off the relegation zone.
"We have a good team, we are in good shape".
"This chapter is over, finished, so we are going to think of the future".
"We're really happy with the victory", said Aguero after registering his 11th treble for the club and his second of the season.
Newcastle's supporters must look at City and wonder how close they are to getting their own rich new owners after a week in which a potential takeover of the club by British businesswoman Amanda Staveley was branded "frustrating and a complete waste of time" by owner Mike Ashley. We have a good team, we are in good shape. "We can learn a lot off them, watching what they do".