It was a piece of brilliance that provided the defining moment of the game, keeping alive Chelsea’s hopes of a top-four finish and delivering another blow to Swansea’s survival prospects on a day that finished with Southampton breathing down their necks. Cesc Fàbregas was the scorer, racking up 50 Premier League goals in style, yet it was the artistry from Eden Hazard that went before which caught the eye just as much as the midfielder’s splendid finish.

Swansea contributed to their own downfall in the build-up to that early goal by carelessly giving away possession inside their own half and, although Carlos Carvalhal’s side finished the match strongly, they were unable to repair the damage as Chelsea collected a third successive away victory in the league to move two points behind Tottenham, who have a game in hand.

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For Swansea the league table now makes for uncomfortable viewing. The four-point advantage they enjoyed over Southampton at the start of the day has been trimmed to a point and momentum seems to have deserted them at a critical stage of the season. Although Carvalhal made the point afterwards that Swansea are in a far better position than when he was appointed in December, they have failed to win in six league matches and for long periods against Chelsea it was hard to see where a goal would come from.

With three fixtures remaining their fate is still in their own hands and it promises to be quite an occasion on Tuesday week, when Southampton come to the Liberty Stadium. Stoke are then the visitors on the final day of the season and it now looks as if this relegation battle will go right to the wire. “If we play like that today, I’m sure we’ll get the necessary points,” said Carvalhal, a little optimistically.

As for Chelsea, this was not a vintage performance from them by any stretch but Antonio Conte’s side did just enough to get over the line. It was not until the final 20 minutes that the champions started to come under any real pressure, after Carvalhal scrapped the three-man central defence that has become more of a hindrance than a help to a team that struggles to create chances, and even then Chelsea looked reasonably comfortable.

The only real moment of concern for Chelsea was when Nathan Dyer tumbled to the ground in the Chelsea area following a robust challenge from Gary Cahill, who squared up to Jordan Ayew in the final seconds of the game after being unhappy with the Swansea forward’s shove on him from behind. Jon Moss, the referee, felt that Cahill got the ball cleanly when he tackled Dyer, although Carvalhal saw things differently. “He took the ball and Dyer together,” the Swansea manager said. “Outside the area it must be a foul; inside the area it must be a penalty.”

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Conte claimed not to have seen the penalty incident and was more interested in discussing Chelsea’s lack of conviction in front of goal. “I think this season we are not clinical,” he said. “In the last period we are winning but also playing a little bit where we could kill the game but instead the game was in the balance until the end.”

Asked why that has been the case with Chelsea this season, Conte replied: “Our top scorer has scored only 12 goals and, if your best scorer has scored only 12 goals, it means it is very difficult to fight for something this season. This is the reality – the stats speak very well.”

Hazard is the man leading the way in the goalscoring charts for Chelsea and it was a wonderful bit of play from the Belgian that created the breakthrough here. Andy King, however, will rue the moment when he allowed a routine pass to slip under his foot deep inside the Swansea half, handing Chelsea and N’Golo Kanté possession.

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Hazard, the best player on the pitch, then picked up the ball and pirouetted away from Ki Sung-yueng with a lovely turn, before driving forward to the edge of the area. All eyes were looking to Hazard’s left but instead he played an exquisite reverse pass that bamboozled the Swansea defence and picked out Fàbregas.

What followed was just as impressive, as the Spaniard, without breaking his stride, swept a glorious first-time left-footed shot that nestled in the top corner.

Pedestrian in possession and hamstrung by a lack of width further forward, Swansea never really troubled Chelsea until that tactical shift and a couple of substitutions led to them attacking with more urgency and conviction. André Ayew and Tom Carroll both shot narrowly wide during that period, but it still seemed a case of too little too late for a team that has a tense couple of weeks ahead.