Edin Dzeko put Manchester City ahead from Aleksandar Kolarov's cross after just eight minutes, but their lead was only intact at half-time thanks to a contentious decision from referee Mike Jones.
Cheick Tiote thought he had equalised with a powerful strike into the top corner from the edge of the area, but the goal was disallowed after Jones consulted with his assistant and ruled that Yoan Gouffran was offside and interfering with play.
Newcastle kept pushing for an equaliser and Joe Hart had to make several important stops in a fiery second half, when Samir Nasri was stretchered off after a challenge by Mapou Yanga-Mbiwa.
Alvaro Negredo then grabbed a second on the counter-attack in stoppage-time to lift City above Chelsea and Arsenal.
City, fresh from their 6-0 Capital One Cup semi-final first leg demolition of West Ham, started well as Kolarov terrorised Yanga-Mbiwa.
It took them just eight minutes to go ahead when David Silva played Kolarov in behind Yanga-Mbiwa and his driven cross was thumped home by Dzeko.
It could have been worse for the Magpies with the in-form Negredo just failing to connect with another Kolarov cross in front of goal and then looping a header on to the roof of Tim Krul's net.
But with Yohan Cabaye, who had started in a No.10 role behind Loic Remy, dropping deeper, the home side took a foothold in the game and gradually stemmed the tide.
Steven Taylor stabbed a Cabaye corner wide, and the Frenchman forced a fine 33rd-minute save from Hart with a rasping shot from a tight angle.
But the resulting corner brought controversy as Newcastle thought they had dragged themselves back level.
The ball was cleared to Tiote on the edge of the box and he unleashed the sweetest of left-foot strikes which left Hart rooted to the spot as it screamed into the back of the net.
The midfielder set off on a joyous run, unaware that Jones was consulting his assistant. Replays confirmed that Gouffran was one of three players in an offside position, and the pair decided the Frenchman was interfering with play, a view not shared by the vast majority of the 49,423 spectators inside St James' Park.
Alan Pardew was certainly of that persuasion and he and Manuel Pellegrini were involved in a heated exchange as the whistle approached.
Buoyed by a sense of injustice, the Magpies returned in determined mood and Vurnon Anita forced a 48th-minute save from Hart.
Moussa Sissoko's pass then put Remy in on goal, but as he tried to turn inside Vincent Kompany rather than shooting first time, he took a touch too many and the chance had gone.
However, City were far from done and Krul had to make a fine block to keep out a point-blank header from Negredo, who had earlier fired high over on the turn.
But Hart had to dive to his right to keep out Cabaye's swerving 59th-minute attempt and then punch away the same player's free-kick two minutes later with the home side dominating.
Cabaye was waging a one-man war on Hart's goal and sent another dipping shot just over with 68 minutes gone, but it was Remy who was denied by the goalkeeper after latching on to Gouffran's cross two minutes later as Kompany and Pablo Zabaleta collided.
Yanga-Mbiwa then picked up a yellow card for a challenge on Nasri, with the City player exiting the pitch on a stretcher.
As Newcastle pushed forward, City exploited the space they left behind and Fernandinho rattled Krul's crossbar with an 87th-minute header.
Remy might have snatched a point with a header which sailed just high and wide from Cabaye's corner and Taylor saw an injury-time shot blocked by Dzeko.
However, Negredo made sure City would displace Chelsea deep into the 95th-minute, despite Krul blocking his initial effort.