Manuel Pellegrini's side wasted no time in taking full advantage of the leaders dropping points in the 1-1 draw at home to struggling Burnley, winning a penalty within 30 seconds of kicking off against the visitors.
They raced into a 3-0 lead within 21 minutes with Edin Dzeko having a hand in all three, scoring his first league goal since September after Sergio Aguero, from the spot, and Samir Nasri had done the early damage.
David Silva scored twice after the break before £28million January signing Wilfried Bony was handed his debut from the bench but was denied a maiden goal by the outstretched leg of goalkeeper Tim Krul.
Ten-man Chelsea slipped up against Bunrley despite defender Branislav Ivanovic's fourth goal in six appearances giving them an early lead after Eden Hazard had brilliantly skipped past four players.
However, Nemanja Matic was dismissed midway through the second half after reacting violently to an excessive challenge by Ashley Barnes, meaning he now misses next weekend's Capital One Cup final.
Nine minutes from time Ben Mee headed in an equaliser from a corner.
Arsenal leapfrogged Manchester United, who slipped to a first defeat in seven matches at Swansea, into third after a 2-1 win at Crystal Palace.
Danny Welbeck had a hand in both goals - both disputed by the Eagles. He was brought down by Papa Souare for Santi Cazorla's eighth-minute penalty, and then had a shot parried by Julian Speroni for Olivier Giroud to convert from close range for his eighth in 11 matches. Glenn Murray notched a late consolation for the home team.
Swansea recorded their first league double over an in-form United, who had taken 34 points from the last 45, by coming from behind to triumph 2-1.
Midfielder Ander Herrera's second goal in six days put the visitors ahead midway through the first half but Ki Sung-yueng, who scored in the 2-1 win at Old Trafford on the opening day, converted Jonjo Shelvey's pass two minutes later before Shelvey drilled home from 30 yards after the break.
Tim Sherwood's first match in charge could not halt Aston Villa's losing run as they slipped to a sixth successive defeat to Stoke.
A glancing header from on-loan Manchester City winger Scott Sinclair - his second in as many games - was cancelled out by Mame Biram Diouf on the stroke of half-time.
Victor Moses then converted a 90th-minute penalty after he was brought down by Ron Vlaar - a challenge which earned the Villa captain a second yellow card.
Barclays Prem
Swansea 2 - 1 Man Utd
Man City 5 - 0 Newcastle
S'land 0 - 0 W Brom
Hull City 2 - 1 QPR
Chelsea 1 - 1 Burnley
C Palace 1 - 2 Arsenal
A Villa 1 - 2 Stoke
Joey Barton was sent off for the ninth time in his career as QPR lost 2-1 at Hull.
The Hoops captain, already on a Premier League record run of seven consecutive yellow cards, was dismissed for a below-the-belt blow on Tom Huddlestone.
QPR striker Charlie Austin, back from injury, scored his 14th of the season to cancel out Nikica Jelavic's 16th-minute opener only for Dame N'Doye to snatch victory a minute from time.
A goalless draw at home to West Brom did little to ease Sunderland's worries near the foot of the table, with Adam Johnson's disallowed goal the closest either side came to breaking the deadlock at the Stadium of Light.