- Man Utd
Manchester United host Brighton, whilst Chelsea visit Leicester in the FA Cup quarter-finals.
Sergio Aguero took centre stage with a finishing masterclass to take his tally in Manchester City's last seven home games to 14 goals.
Conte's side produced a limp display that could easily have seen them beaten by a Leicester team who missed a host of first-half chances.
The Clarets thought they had rescued a point when they equalised on the 87th minute, but Ragnar Klavan met Dejan Lovren's header in the final moments.
Mohamed Salah was again instrumental for Liverpool as he took his tally to 17 Premier League goals this season.
Manchester United paid for wasting some chances when Marc Albrighton crossed and Harry Maguire headed home in the final seconds.
Manchester City held their nerve to edge through 4-3 on spot-kicks after the two sides were locked at 1-1 following extra time.
Craig Shakespeare, 53, was promoted from his role as assistant coach on an interim basis following the shock dismissal of Claudio Ranieri in February and in June he was handed a three-year contract.
Riyad Mahrez's first Premier League goal of the season secured Leicester a 1-1 draw with West Brom on Monday but it was not enough to lift the 2016 champions out of the bottom three.
Arsenal legend and former FC Goa player Robert Pires will return to India to meet local EPL fans, where he will be joined by former Everton star Graham Stuart.
Leicester's Shinji Okazaki sent Liverpool crashing out of the League Cup, while Tottenham edged past Barnsley to reach the fourth round on Tuesday.
Fellaini added a late second from Jesse Lingard's cross-shot to send Jose Mourinho's side back to the top of the table after Huddersfield Town briefly overtook them by drawing with Southampton earlier in the day.
Sam Vokes scored twice as Burnley torpedoed defending champions Chelsea 3-2 at Stamford Bridge on Saturday in one of the most sensational opening-weekend results in English top flight history.
Arsenal host Leicester in the opening game of the hotly-anticipated new season of the Premier League.
Machester City went past Leicester City 2-1 as Swansea beat Sunderland 2-0 to boost their survival bid while Southampton ended their barren run against Middlesbrough on Saturday.
Jamie Vardy scored the goal that effectively ensured Leicester City would remain in the Premier League as the outgoing champions won 1-0 away to West Bromwich Albion.
Jamie Vardy scored in vain as Leicester City's Champions League fairytale came to a valiant end following a 1-1 quarter-final draw at home to Atletico Madrid on Tuesday.
Vincent Janssen bagged a rare goal in second-half stoppage time as Tottenham Hotspur chalked up seven successive league wins for the first time since 1967.