Curtin Jones's 71st-minute strike saw Liverpool edge past Everton in a derby tie at Anfield.
Arsenal closed the gap on leaders Liverpool with a 2-1 Premier League victory at Nottingham Forest
Chelsea have completed the signing of Basel's Egyptian winger Mohamed Salah, the Premier League club said on their website on Sunday.
"I think he's our best player," Fabregas said.
Manchester United will be back in action in next season's Champions League after they hammered Chelsea 4-1.
Real Madrid beat holders Manchester City in an edge-of-your-seat 4-3 shootout victory to reach the semi-finals of the Champions League.
IMAGES from the Premier League matches played on Saturday
Two Robin van Persie goals earned the Gunners a 2-1 victory as Chelsea slid to a second home league defeat of the season.
Chelsea, however, were unlucky after they were again denied by the woodwork.
English Premier League side Chelsea completed the signing of Argentina midfielder Enzo Fernandez from Benfica for a British record 106.8 million pounds ($131.46 million).
He has been charged by the FA for remarks against match-officials
Diego Costa has accused Chelsea of treating him like a "criminal" in a forthright newspaper interview which will deepen the breach with the Premier League club.
Chelsea playmaker Eden Hazard relishes playing with striker Diego Costa and is keen for the Spaniard to resolve his stand-off with the English Premier League champions and return to action.
The victory, Chelsea's 28th of the season, put the long-time league leaders 10 points clear of second-placed Tottenham Hotspur, who have only three games left to play.
Chelsea have enough experience to keep their composure in the title race after Sunday's 2-0 defeat at Manchester United cut their lead at the top of the Premier League table to four points with six games left, goalkeeper Asmir Begovic has said.
Buoyant Chelsea extended their Premier League lead and calmed nerves at Stamford Bridge with a 4-2 win over Southampton on Tuesday that moved them seven points clear of their nearest pursuers Tottenham Hotspur.
IMAGES from Premier League matches played on Saturday.
Chelsea must improve their defensive solidity if they are to challenge for silverware this season, winger Eden Hazard has said. Despite coach Antonio Conte's reputation of building teams around a solid defensive unit, Chelsea have conceded nine league goals this season, including three against Arsenal on Saturday, the first of which came from an error by Gary Cahill. The London club have kept just one clean sheet in six league games this campaign.
Arsenal's Pierre-Emerick Aubameyang struck a vital late goal to seal a 3-1 win over Valencia on Thursday and give his side breathing space for the second leg of their Europa League semi-final in Spain next week.
His first overseas coaching adventure -- Maurizio Sarri has chosen a devilishly difficult league to try and make it happen and a club not exactly known for its patience.
Tottenham Hotspur denied Chelsea a record 14th consecutive Premier League win and loosened their grip on the title race as two Dele Alli headers secured a 2-0 victory.
Manchester United and Tottenham Hotspur are second and third respectively, a point ahead of Antonio Conte's men.
Antonio Conte's title ranks as one of the finest of the Abramovich era because this title was so unexpected. Out of the blue, in fact.
Jose Mourinho has confirmed Diego Costa was taken to hospital with a rib injury suffered during Chelsea's Capital One League Cup match at StokeCity on Tuesday.
The 36-year-old former England international played over 700 games for Chelsea and has been their most successful captain.
Napoli president Aurelio De Laurentiis said on Wednesday that the English Premier League side are close to securing a deal for former Napoli boss Maurizio Sarri to replace Conte.
Chelsea manager Antonio Conte is keen to see how his side cope with the absence of striker Diego Costa and midfielder N'Golo Kante and may change his favoured 3-4-3 formation when Bournemouth visit.
Chelsea manager Jose Mourinho believes that not having another international break until March will help his team recapture their best form after a woeful start to the season.
Chelsea winger Eden Hazard still hopes he can one day fulfil his dream of playing for Real Madrid.
Images from the English Premier League London derby played between Arsenal and Chelsea at the Emirates on Wednesday
Manager Guus Hiddink dismissed speculation that Eden Hazard will leave English Premier League champions Chelsea, insisting that the winger is content to stay at Stamford Bridge.
Images from the EPL matches played on Sunday
Manchester United's Alejandro Garnacho scored with a magical overhead kick in the third minute to send the visitors on their way to a 3-0 victory over an Everton team already reeling in their first Premier League game after being docked 10 points.
Daryl Janmaat, Gerard Deulofeu and Roberto Pereyra all scored late on in response to Eden Hazard dragging Chelsea back into the game with a curler in the 82nd minute after Tiemoue Bakayoko was sent off for a second booking on the half-hour.
Images from EPL matches played on Saturday.
A summary of Wednesday's matches in the UEFA Champions League.
Chelsea manager Maurizio Sarri said having Eden Hazard in such unstoppable form makes winning "easy" but appears almost resigned to losing him.
Manchester City and Arsenal closed in on Premier League leaders Liverpool with contrasting victories on Saturday as Manchester United's bubble was burst by Fulham.
Chelsea's struggle to retain the title is hardly surprising as the club returned to the Champions League and their league rivals strengthened their squads, former Leicester City manager Claudio Ranieri has said.
Salah joined Chelsea under Mourinho in 2014 but failed to establish himself at Stamford Bride and was loaned out to Fiorentina and Roma before a permanent move to the Stadio Olimpico outfit in 2016.
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