Queens Park Rangers gave a good account of themselves defending resolutely for the most part of the match. However, a costly error by QPR goalkeeper Rob Green in the 88th minute was punished by the visiting team.
The winner was scored by Spanish international Cesc Fabregas, who slotted a pass from Eden Hazard into the bottom right corner of the goal.
While Chelsea maintain their lead at the top, the loss has meant that QPR continue to languish in the bottom three.
In the championship standings, Chelsea are followed by Arsenal, who won their match against bottom-placed Burnley with an identical 1-0 margin on Saturday.
Aaron Ramsey was the only goal scorer in what was a scrappy encounter.
"It was a battling performance more than a fluid performance, and that was because Burnley are perfectly organised and very fit to keep their shape for the full 90 minutes," Arsenal manager Arsène Wenger remarked after the match.
The two London clubs are followed by the two Manchester teams, United and City who clash on Sunday evening.
Defending champions Manchester City will have to produce a sparkling performance not only to beat their local rivals but also to give a boost to their campaign for the remainder of the season.
City’s disappointing performance this season was reflected in their manager Manuel Pellegrini’s comments of his team having thrown their campaign "into the garbage".
City have been eliminated from both the FA Cup and the Champions League and they have little hope of retaining the Premier League title because of recent losses to Arsenal, Liverpool, Burnley and Crystal Palace.