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Villa's inability to open up the defence was in stark contrast to El Kaabi, who only needed the slightest sniff of a chance against the English side to put the ball in the net.
Fourth-placed Aston Villa suffered a 3-1 home defeat by Newcastle United, Crystal Palace came from behind to beat visiting Sheffield United 3-2 and struggling pair Fulham and Everton fought out a goalless draw at Craven Cottage.
Arsenal's second league defeat of the season leaves Mikel Arteta's men one point behind Liverpool, who went top with a controversial 2-1 win at Crystal Palace earlier on Saturday.
Potter is the 12th manager to be sacked in the Premier League this season with the announcement coming hours after relegation-threatened Leicester City parted ways with Brendan Rodgers by mutual agreement.
Third-placed Chelsea, who had drawn with Everton and Wolverhampton Wanderers in their previous two games, are now level with second placed Liverpool on 41 points -- six behind leaders Manchester City.
A superb individual effort by midfielder Jacob Ramsey and a late Ollie Watkins goal gave Aston Villa a 2-0 win at bottom team Norwich City.
Norwich sacked Farke this month when Smith was also fired by Villa following a run of five straight league defeats.
The 41-year-old, who played more than 700 games for Liverpool between 1998 and 2015 and won nine trophies at the Anfield club, last season guided Rangers to their first Scottish league title since 2011.
The victory also broke a three-match losing streak for City against Chelsea, the most recent in the Champions League final in Porto in May.
Chelsea beat Aston Villa 3-0 for their 600th Premier League victory to move joint top of the standings alongside Manchester United.
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