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David Silva struck twice for Pep Guardiola's side as they went past Arsenal's 14-match winning sequence, although unlike the London club's, City's streak has been in a single season.
Manchester United kept up a distant pursuit as they toiled to a 1-0 defeat of Bournemouth at Old Trafford to remain 11 points adrift in second place, Romelu Lukaku's ninth league goal of the season proving just enough.
Liverpool and Arsenal could only draw 0-0 with struggling West Bromwich Albion and West Ham United respectively, allowing Tottenham Hotspur to move into fourth spot behind Chelsea thanks top a 2-0 win over Brighton and Hove Albion as Serge Aurier scored his first goal for the club.
City have 49 points to United's 38 with champions Chelsea, who won at Huddersfield Town on Tuesday, on 35. Tottenham have 31, ahead of Liverpool on goal difference while Arsenal dropped to seventh with 30 points.
It was an enjoyable night for managers returning to former clubs as Sam Allardyce watched his Everton side win 1-0 at Newcastle United and Claude Puel's fast-improving Leicester City triumphed 4-1 at Southampton, the club who sacked him at the end of last season despite taking them to the League Cup final.
City hardly broke sweat as they turned their trip to south Wales into a training session despite making four changes to the side that won 2-1 at Manchester United on Sunday.
Silva opened the scoring from Bernardo Silva's cross and Kevin De Bruyne made it 2-0 with a free kick.
It was all over when the silky Silva played a one-two with Raheem Sterling to make it 3-0 early in the second half with his fourth goal in his last three games.
Sergio Aguero, back in the side with Gabriel Jesus rested, fired past Lukasz Fabianski to complete another masterclass from Guardiola's City slickers.
While the purists are purring at City's form, you could only sympathise with Swansea boss Paul Clement who summed up what many of his peers might be feeling.
"At times it was horrible to be on the sideline watching that, seeing my side trying but suffering for long periods," he said.
"It was hard to watch at times because they were so dominant. One of the best sides I've ever come across."
United looked flat after their chastening defeat against City and were indebted to Lukaku's powerful header and several good saves by David de Gea against a plucky Bournemouth.
Manager Jose Mourinho, distracted by reports of a fracas after the City defeat in which he was reported to have had milk thrown at him, admitted his side had been low on energy.
"It was difficult match. They had one more day's rest than us, they were fresher than us, and mentally fresher because a big match takes more from our players," he said.
"They were difficult opponents and difficult conditions. If we had scored the second it would have been a calm night."
Liverpool were left to rue a late disallowed goal for Dominic Solanke as they could find no way past West Brom, their second home draw in four days.
"We can do better and we have to do better but on a night like this when you are not at your best you need a bit of luck," manager Juergen Klopp said.
Shinji Okazaki scored twice for Leicester as they racked up a fourth consecutive win, while Wayne Rooney earned Everton a 1-0 win at Newcastle United whose night ended in depressing fashion with a red card for Jonjo Shelvey.