Leaders Chelsea offered a chink of light to City after a stormy game at Stamford Bridge where Nemanja Matic was sent off for retaliating to an awful challenge from Burnley's Ashley Barnes and the hosts were denied two strong penalty claims.
City then made the most of their lifeline, emphatically exposing Newcastle's failings with two goals from David Silva among the highlights of a crushing victory that reduced their deficit at the top of the Premier League to five points.
It was another ominous display from second-placed City who have scored nine goals in their last two games and look back to their very best.
Arsenal climbed to third with a 2-1 win at Crystal Palace, above Manchester United who fell to defeat at Swansea City by the same scoreline.
Tim Sherwood's first match as Aston Villa manager ended in disappointment as his new charges squandered a first-half lead to lose 2-1 at home to Stoke City who scored a stoppage-time penalty from Victor Moses to snatch the points.
At the bottom of the table, Hull City moved four points clear of the relegation zone with a 2-1 win over fellow strugglers Queens Park Rangers who had midfielder Joey Barton sent off in the first half.
Sunderland and West Bromwich Albion drew 0-0.