Manchester City survived a lacklustre performance to edge a 10-man Wolves in the early kick-off, before Chelsea and Liverpool followed that up with three points of their own in narrow wins over Leeds United and Aston Villa.

Man City 1-0 Wolves

Pep Guardiola saluted Raheem Sterling’s “massive contribution” to Manchester City after the forward scored his 100th Premier League goal to give the leaders a 1-0 win over 10-man Wolves on Saturday.

Sterling netted from the spot in the second half at the Etihad Stadium to clinch City’s sixth successive league victory.

City’s cause was aided by a needless first-half red card for Wolves striker Raul Jimenez, who was dismissed for failing to retreat the required 10 yards before a free kick he had been booked for conceding seconds earlier.

Sterling’s landmark goal ensured City capitalised on Jimenez’s blunder as they survived an average display to get back on track after the midweek Champions League defeat at Leipzig.

Liverpool 1-0 Aston Villa

Liverpool ensured there was no happy return to Anfield for Steven Gerrard as Mohamed Salah’s second-half penalty earned a 1-0 win over Aston Villa.

Tyrone Mings was roped into a clumsy challenge on Salah and Liverpool got their spot kick in the 67th minute after a wave of pressure over the opening hour.

Martinez has earned a reputation as a penalty specialist, but Salah’s strike was too precise for the Villa stopper despite guessing the right way.

Going behind suddenly sparked Villa into life as Gerrard introduced Danny Ings and Emiliano Buendia to offer more of an attacking threat.

And they too had a big appeal for a penalty turned down late on when Alisson’s attempted clearance rebounded off Matip towards his own goal and the Brazilian goalkeeper escaped unpunished from a collision with Ings.

Chelsea 3-2 Leeds United

Jorginho held his nerve to score a stoppage-time penalty as Chelsea snatched a dramatic 3-2 win over Leeds on Saturday.

Thomas Tuchel’s side bounced back from their two-game winless run but not before surviving a major scare at Stamford Bridge.

Leeds went ahead through Raphinha’s first-half penalty and Chelsea drew level thanks to Mason Mount’s strike.

Jorginho, playing through the pain of a recurring back problem, netted the first of his two penalties after the interval, only for Leeds teenager Joe Gelhardt to equalise with seven minutes left.

Deep into stoppage time, Italy midfielder Jorginho struck again from the spot after Mateusz Klich’s challenge on Antonio Rudiger.

It was a vital victory for Chelsea after their top-flight defeat at West Ham and midweek draw with Zenit Saint-Petersburg in the Champions League.

With leaders Manchester City and second-placed Liverpool both winning on Saturday, Chelsea remains in third place, two points adrift of first place.