Edin Dzeko's goal midway through the second half has sent Manuel Pelligrini's side into first, two points clear of Arsenal.
City's neighbours Manchester United enjoyed a 1-0 win at Norwich City; Danny Welbeck's goal on 57 minutes proved the difference at Carrow Road.
Aston Villa and Swansea played out a 1-1 draw.
Gabbie Agbonlahor's goal after 7 minutes was cancelled out by Roland Lamah half an hour later.
Hull City hammered Fulham 6-0 at the KC Stadium.
A Robert Koren double was added to by Elmohamady, Boyd, Huddlestone and Fryatt.
Earlier West Ham and West Brom played out a 3-3 draw at Upton Park. Joe Cole had given the home side an early lead, but that was cancelled out by two goals from Nicolas Anelka.
Strikes from Modibo Maiga and Kevin Nolan then put West Ham into a 3-2 lead, before Saido Berahino earned the Baggies a point.
The point keeps West Ham in the relegation zone, with West Brom in 15th.
Later, Cardiff City host Sunderland from half five.
