Chelsea defeated Fulham, a Premier League competitor from West London, by a slim margin at Stamford Bridge thanks to a penalty kick from Cole Palmer in the first half.
Raheem Sterling was set up by Palmer's reverse pass, and Issa Diop caught him inside the penalty area.
Palmer scored his ninth goal since joining the Blues in August, sending Fulham keeper Bernd Leno the wrong way with a well-executed penalty kick.
Conor Gallagher nearly scored a late second with a well-placed shot that cannoned off the far post with the outside of his boot.
Chelsea moved up to ninth place in the standings by holding Fulham at a distance and holding on for their third straight victory.
The visitors, who have dropped four of their last five games, remain in 13th place.
Even if it wasn't a classic, Chelsea managed to win three points.
Chelsea wasted opportunities in their 1-0 loss to Middlesbrough in the first leg of the Carabao Cup semi-final on Tuesday, and they again had trouble scoring goals in the first half of their match against Fulham.
After sixteen minutes, Armando Broja headed a cross from Enzo Fernandez wide of the near post, and Gallagher missed with a shot over the bar.
To break the tie, it needed the combined calm of Palmer and Sterling, who made Diop make a tackle he didn't have to.
Chelsea appeared much more confident after the restart. In the fiftieth minute, Fernandez crossed the ball for Sterling, and the England striker flicked his header against the post, but any finish would have been disallowed for offside.
With the win, Mauricio Pochettino's team achieved a first since July 2020—winning four straight home league games.
Chelsea's 2024 league campaign is off to a flawless start, with their semi-final second leg against Middlesbrough on January 23. This comes after they won just 12 of their 43 league games in 2023, the fewest wins they had in a calendar year since 1995.
The awful away form for Fulham persisted. The Cottagers were defeated 2-1 at Liverpool in the EFL Cup on Wednesday, and they have now dropped their last five away league games.
Marco Silva's side had the finest chance of the first exchanges when Antonee Robinson's low cross found Harry Wilson at the back post, but the winger's effort from a tight angle was pushed away by the foot of Chelsea keeper Djordje Petrovic.
After Raul Jimenez of Fulham met Andreas Pereira's cutback in the 74th minute, Petrovic brilliantly stopped the forward with a spectacular diving save to his right.
If referee Anthony Taylor had decided to send Chelsea defender Malo Gusto off with the game tied at goal in the 39th minute, the result of the match might have been different.
The video assistant referee (VAR) was glad to support Taylor's decision to show Gusto a yellow card even though the France right-back caught Willian above the ankle.
On January 24, the second leg of the semi-final pits Fulham against Liverpool.