Antonio Conte's men have managed to bring home three important points after they easily defeated troubled Swansea by 1-0 on Wednesday night.
Chelsea took the lead thanks to former Roma defender Antonio Rudiger, who headed the ball home for the guests in the opening minutes of the second half.
The Blues crucially needed to win this game in order to keep their title race hopes alive, while Swansea were looking for points to keep away from the relegation zone and initially seemed boosted by the weekend's draw to Bournemouth.
The London club proved to be still on the run for the title even though they struggled to be effective, creating several chances, but only managing to net once.
Paul Clement's Swansea, on the other hand, had sporadic chances to counterattack the reigning Premier League champions and keep on languishing in the relegation zone.
The hosts had a quite explosive start after being awarded a very interesting free-kick a few inches from the box. Willian - one of Chelsea's best players this year - curled in a wonderful cross, which, however, Alonso missed by a whisker.
Towards the half-hour mark, Morata missed a delicious chance to score as he received a ball in the middle of the box and provided a marvelous first-time strike in an almost nonchalant way. The ball went slightly above the bar.
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Usual bencher Pedro was extremely proactive during the first half, usually working the engine behind most of Chelsea's actions.
Shortly before the half-time whistle, he approached the box and looked for a space to shoot. Although there didn't seem to be any, the Spaniard found one, but his thump was easily gathered by Fabianski.
Although the Blues basically conducted a one-way match for the whole first half - Swansea failed to create any chance at all - Chelsea boss Conte looked frustrated as usual, but his several complaints to the referee were judged over the line towards the end as the Italian was eventually sent off.
Not much changed during the initial minutes of the second half. Swansea looked tired and lifeless as they stoically defended while Chelsea orchestrated their games. The Blues managed to break the deadlock after less than ten minutes when Rudiger was provided with a magnificent cross by Kante. His diving header gave them a well-deserved lead.
Seconds later, Alonso missed a magnificent chance to double the score after picking up from Pedro's previous attempt. However, Van Der Hoorn was ready and blocked the stroke.
Morata too was close to scoring the second for Chelsea after Fabregas served a stunning free kick just on his head, but the shot was brilliantly parried by Fabianski.
Alonso once again proved to be one of the most threatening defenders of the league as he nearly netted for Conte's side around 70 minutes inside the second half. The former Fiorentina man dribbled a few Swans in the box and kicked a left-footed strike that, however, Fabinho gathered again.
Swans made some weak attempts on their own after the goal and finally managed to show their determination. However, they were never sufficiently effective to create a real danger for Courtois and the defense, who were always prepared to fight them back.
Chelsea returned to Stamford Bridge after almost one month away, the last game at home being the 1-0 win against Manchester United.
The Blues had lost only one of their 12 Premier League encounters against the Welsh side.
Eden Hazard was the big missing name of the match, as Conte opted to let him rest in favour of Pedro, but then inserted the Belgium talisman in the second half.
Swansea had to without summer signing Tammy Abraham, who couldn't play against his parent team.