Carlo Ancelotti's Chelsea came from behind to win 3-1 at Sunderland on Tuesday and make it two wins from two in the Premier League.
Arsenal, Manchester City and Liverpool also joined Chelsea in the quarter-finals of the League Cup.
Frank Lampard has been named Chelsea's Player of the Year for a record third time. The England midfielder is the first player to win the accolade three times, the English Premier League club said on Friday.
Midfielder Frank Lampard could miss champions Chelsea's Premier League opener at home to West Bromwich Albion on Saturday.
Chelsea have told Inter Milan they are not prepared to consider any approach for England midfielder Frank Lampard. The Stamford Bridge club confirmed they had received an approach from the Italian champions but denied media reports that an offer had been made for the 30-year-old who has 12 months remaining on his contract.
Chelsea midfielder Frank Lampard is very keen to join Inter Milan, the Italian club's director Gabriele Oriali said on Thursday. Chelsea said this week they would not enter into negotiations with the Serie A champions over the England player, who has a year left on his contract.
Frank Lampard underlined his value to Chelsea with a well-taken double that secured a 2-1 comeback win at Everton on Sunday to move the Londoners back up to third place in the Premier League.
England claimed a memorable and unlikely 1-0 win over World champions Spain thanks to a headed goal from Frank Lampard and some resolute defending during the closing stages of a hugely entertaining friendly at Wembley Stadium on Saturday.
Frank Lampard, Chelsea's all-time leading scorer, netted against his old club when he came on as a late substitute for Manchester City to give the champions a 1-1 draw.
Chelsea's interim manager Rafa Benitez has said he expects the club's long-serving England players Frank Lampard and Ashley Cole to leave Stamford Bridge at the end of the season, British media reported on Saturday.
Frank Lampard came off the bench to convert a late penalty as Chelsea beat Manchester City 2-1 on Monday to inflict the Premier League leaders' first defeat of the season and lift themselves back into title contention
'It has been good on pitch and off pitch,' Lampard said.
Lampard was handed a three-year contract having left second tier Derby County.
Chelsea manager Frank Lampard believes his side are a long way short of the levels of Premier League Champions Liverpool and Manchester City, who have set the benchmark in terms of consistency. Lampard's Chelsea, currently third in the league, visit title winners Liverpool on Wednesday, chasing the three points they need to secure Champions League football next season.
Frank Lampard's hat-trick inspired Chelsea to a 5-1 thumping of Bolton Wanderers and Tottenham Hotspur poured more misery on Arsenal with a 2-1 victory in a controversial north London derby in the Premier League on Sunday.
Arsenal manager Arsene Wenger has apologised for shoving his Chelsea counterpart Jose Mourinho on the touchline during a Premier League match at Stamford Bridge.
Wayne Rooney will be given the opportunity to captain England for the first time in a competitive international in their World Cup qualifier against San Marino after Frank Lampard was ruled out of the match through injury.
England coach Fabio Capello will be without at least six of his first-choice side for Wednesday's friendly against Germany in Berlin after midfielders Frank Lampard and Steven Gerrard withdrew from the squad on Monday.
Frank Lampard broke Chelsea's all-time scoring record with two goals as the European champions all but secured a top-four finish in the English Premier League with a 2-1 win in an incident-packed game at Aston Villa on Saturday.
Jose Mourinho's return for a second spell as manager has brought a new feeling of unity at Chelsea, according to club stalwarts Frank Lampard and John Terry.
Callum Hudson-Odoi's positive test last week had prompted the London club to partially close their Cobham training centre, with the first-team squad and coaching staff asked to self-isolate as a precaution.
Frank Lampard underlined his importance to England with a superb winner in his side's 2-1 victory over Brazil in Wembley on Wednesday but his chances of reaching the 100-cap milestone could be scuppered by a move out of Europe, coach Roy Hodgson said.
Frank Lampard began to think there was no way back for Chelsea in the Champions League final as the minutes ticked down with Bayern Munich leading 1-0, but when the match went to a penalty shootout he had no doubts the trophy was coming to London.
Frank Lampard's goals have ensured he will always have a fond place in Chelsea fans' hearts but with no contract extension on the horizon his future at the heart of the club looks increasingly doubtful.
Chelsea will have a massive void to fill in midfield next season after the club's all-time record goalscorer Frank Lampard announced on Monday he was ending his 13-year spell at Stamford Bridge.
Images from the EPL matches played across England on Sunday.
Frank Lampard and Edin Dzeko scored twice as holders Manchester City sailed into the English League Cup fourth round with a crushing 7-0 win over Sheffield Wednesday and Chelsea beat Bolton Wanderers 2-1 on Wednesday.
Frank Lampard, Chelsea's all-time record scorer, came on as a late substitute for Manchester City and scored their equaliser in a 1-1 draw at the Etihad as the champions ended his former club's perfect start to the Premier League season on Sunday.
Chelsea returned to the top of the Premier League when they convincingly beat Birmingham City 3-0 at Stamford Bridge on Wednesday.
His agent Bo Gustavsson told Reuters he had passed away Monday morning.
"I believe before his contract ends Chelsea will offer him an agreement until the end of his career," said Mourinho.
Frank Lampard broke Chelsea's all-time scoring record with two goals as the European champions all but secured a top-four finish in the Premier League with a 2-1 win in an incident-packed game at Aston Villa on Saturday.
Frank Lampard's loan spell at Manchester City is due to end in January but the Premier League champions might want to delay his departure across the Atlantic to enhance their chances of fighting his old club for the title.
Chelsea's veteran midfielder Frank Lampard wants to play on for two or three more years but says this campaign could be his last at Stamford Bridge.
Frank Lampard scored from the penalty spot as Chelsea restored their three-point lead in the English Premier League with an unconvincing 2-1 home win against bottom club Portsmouth at Stamford Bridge in London, on Wednesday. Champions Manchester United had pulled level on points after beating a weakened Wolverhampton Wanderers 3-0 on Tuesday in manager Alex Ferguson's 900th league game in charge.
Chelsea reached the League Cup quarter-finals thanks to two own goals in a 3-2 win over second-tier Derby County on Wednesday as Frank Lampard's return to his former club ended in disappointment.
English cricket's leading Test wicket-taker James Anderson and former England football midfielder Frank Lampard were given the OBE.