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City's loss at Anfield before the international break made this a key game for them but they were made to work for their three points by Frank Lampard's enterprising side.
Chelsea sliced open City's defence in the 22nd minute with Mateo Kovacic superbly picking out N'Golo Kante's forward burst and the French midfielder held off compatriot Benjamin Mendy before smartly slipping the ball past the advancing Ederson.
But six minutes later Belgian midfielder Kevin De Bruyne brought the champions level when the ball fell to him on the edge of the box and he cleverly wrongfooted the Chelsea defence before unleashing a low drive which took two deflections before rattling past wrongfooted Chelsea keeper Kepa Arrizabalaga.
Chelsea had looked the slicker and sharper of the two teams -- and indeed enjoyed the rare status of having more possession at the Etihad - but it was Guardiola's side who went in with the advantage at the break.
Riyad Mahrez cut in from the left and, with Chelsea's defence backing off, he drove a left-foot shot into the far bottom corner to make it 2-1.
Chelsea nearly put themselves out of the game two minutes before the break when Kepa gifted the ball to Sergio Aguero but the Argentine's shot from distance crashed off the bar.