Sergio Aguero opened the scoring for City in the first half before the Magpies scored two goals in the second half through Salomon Rondon and Matt Ritchie.
City remain in second place with fifty six points, four behind Liverpool. Elsewhere, Manchester United scored two late goals to secure a two all draw against Burnley and remain unbeaten under Ole Gunnar Solskjaer.
Arsenal bounced back to winning ways with a 2-1 win over Cardiff at the Emirates.
In transfer news, Arsenal are close to completing the signing of Barcelona midfielder Denis Suarez.
The Spaniard will join the Gunners on loan until the end of the season, with a purchase option in the summer. Suarez has played 71 times for Barcelona since joining in 2013 but has only featured eight times this season.
He previously played under Gunners manager, Unai Emery during a loan spell at Sevilla when Emery was in charge of the La Liga side. Arsenal had targeted Suarez throughout the January transfer window but their pursuit was complicated by wanting the deal to include only an option to buy and Barcelona demanding it be an obligation.