Young international winger Cole Palmer (21 years old) scored the winning goal for the West London team from a penalty kick in stoppage time in the first half after a challenge on Raheem Sterling (45 + 4).
Palmer converted the fifth penalty kick this season, putting his team back on the path to victory after the disappointment of losing to Middlesbrough from the second level last Tuesday in the first leg of the League Cup semi-final.
Chelsea temporarily advanced to eighth place in the league with 31 points, while Fulham’s balance froze at 24 points in 13th place.