Chelsea ended a run of three games without a win across all competitions by beating Villa, but it was hardly the kind of convincing win that Frank Lampard's young squad had been delivering until recently.
West Ham registered their first win at Stamford Bridge in 17 years after Aaron Creswell scored the sole goal of the game in the second half.
It took a while for Christian Pulisic and Mateo Kovacic to establish themselves at Chelsea, prompting doubts about the wisdom of their recent big-money arrivals.
Christian Pulisic’s third Champions League goal and Kepa Arrizabalaga’s penalty save weren’t enough to secure Chelsea a spot in the knockout stage of the European competition on Wednesday.
Kevin De Bruyne and Riyad Mahrez were on target for the current Premier League champions as Manchester City maintained pressure on Liverpool.
Chelsea manager Frank Lampard has implemented a strict disciplinary regime for the young squad, including a range of fines that vary according to the indiscretion.
Palace's defence survived a Chelsea onslaught at Stamford Bridge in the first half — the Blues recording 11 shots to zero for Palace at the break.
In a roller-coaster match at Stamford Bridge, Frank Lampard's side scored two own goals and two penalties while Ajax had two players sent off as the game finished 4-4.
Christian Pulisic scored in his second Premier League game in a row while Tammy Abraham continued his fine form as Chelsea beat Watford 2-1 on Saturday.
Liverpool knocked out Arsenal in the pre-quarters of the League Cup 5-4 via penalties after the game ended 5-5 after normal time while Marcus Rashford's brace sent Manchester United to the next round.
Chelsea vs Manchester United Live Streaming: Watch Carabao Cup, round 3 live football match online on JioTV and TV telecast on Colors Infinity HD.
Christian Pulisic's hat trick was a second by a US player in league history after Clint Dempsey scored three in Fulham's 5-2 defeat of Newcastle in 2012.
Alonso broke the deadlock in the 73rd minute at Stamford Bridge as the Blues earned their fifth straight victory in all competitions.
Tammy Abraham, Mason Mount and N'Golo Kante scored in the first half, before Christian Pulisic set up fellow substitute Michy Batshuayi for Chelsea's fourth goal in the 89th minute.
Manchester United won 5-3 via penalties against third-tier English side Rochdale while Chelsea thumped seven past Grimsby Town in the third round of League Cup.
Chasing a first English title since 1990, Liverpool claimed a sixth successive league win at the start of the season after Chelsea were unpicked twice from set-pieces in the first half.
Rodrigo's strike was the 14th goal Chelsea has conceded in the seven games in all competitions since Frank Lampard took charge of the club.
Belgian star Eden Hazard, who joined Real Madrid this summer after seven seasons at Chelsea, revealed the key difference between the supporters of both the clubs.
Not counting own-goals, Chelsea became the first-ever team to have 11 straight Premier League goals scored by players aged 21 or younger.
Liverpool defeated Burnley 3-0 while Sheffield United came back from being 2-0 down to earn a point against Chelsea at Stamford Bridge.
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