Three days after they won the League Cup, Manchester United trailed to Said Benrahma's 54th-minute goal at Old Trafford but an own goal by West Ham's Nayef Aguerd and late strikes from Alejandro Garnacho and Fred sent the hosts into the last eight.
The top two teams in the Premier League cancelled each other out in the first half, with Erling Haaland twice going close for City while pacesetters Arsenal forced home goalkeeper Stefan Ortega into two fine saves to keep them at bay.
Everton slipped into the relegation zone after a 4-1 home defeat by Brighton & Hove Albion on Tuesday and were booed off the pitch but after a sixth defeat in seven matches, Lampard insisted he was not worried about his job.
Guardiola's side will look to reach the FA Cup semi-finals on Sunday when they travel to Southampton for their last eight tie.
In-form Chelsea will fancy their chances at Wembley in a match that could serve as a dress rehearsal for the Champions League final.
Southampton dumped FA Cup holders Arsenal out of the competition on Saturday, winning 1-0 courtesy of a Gabriel own goal.
Manchester United and Liverpool lock horns for the second Sunday in a row this weekend.
Manchester City owner Sheikh Mansour bin Zayed Al Nahyan is the new owner of the oldest existing version of the FA Cup trophy.
The Spanish coach celebrates his one-year anniversary as Arsenal manager on Sunday, a day after their Premier League clash against Everton at Goodison Park.
Arsenal won the title for for a record 14th time and secured their spot at Europa League next season.
Arsenal are desperate to win the title and secure a spot at Europa League to save their season.
Arsenal were outclassed 4-1 by Chelsea in the Europa League final in Baku last year.
Mikel Arteta offered further evidence that Arsenal may have found the manager to lead them back to glory as he masterminded a 2-0 win over his former club Manchester City in the FA Cup semi-final at Wembley on Saturday.
Liverpool’s under-23 manager Neil Critchley has credited James Milner with helping inspire the club’s youngest-ever starting side to their FA Cup fourth-round victory against Shrewsbury Town on Tuesday.
Arsenal teenager Bukayo Saka scored one goal and set up another as the Londoners sealed a place in the FA Cup fifth round with a 2-1 win over Bournemouth at the Vitality Stadium on Monday.
Liverpool’s 18-year-old midfielder Curtis Jones celebrated a dream first goal for the club when his spectacular shot was enough to defeat derby rivals Everton in the FA Cup third round on Sunday.
The Video Assistant Referee (VAR) system will undoubtedly cause controversies in its English top-flight debut next season but any flaws will be ironed out in future, the Premier League’s interim chief executive Richard Masters has said.
Manchester City star Kevin De Bruyne understands Liverpool players being disappointed at falling just short of winning the Premier League title but he does not have any sympathy for them.
The FA said each club will be allocated approximately 33,000 tickets for their fans and tickets are priced in the range of 30 pounds ($39.83) to 80 pounds.
Wolverhampton Wanderers reached the FA Cup semi-finals for the first time since 1998 by beating last year's runners-up Manchester United 2-1 with a clinical second-half display in an intense atmosphere at their Molineux stadium on Saturday.