Costa latched on to a wonderful through ball from Fabregas, before chipping the onrushing Wojciech Szczęsny, to continue his fine goalscoring form.
It was another display of the finishing touch that Costa has brought to this Chelsea side and Fabregas admitted that he is already a very important player for the team - although the Spaniard believes everyone played their part.
"Obviously Diego is a great striker, he can hold the line and he is a very important player," Fabregas said to Chelsea's official site. "But we all played our part."
"As a team we were solid and comfortable with the ball. We had difficult moments during the game but we solved them well. We wanted six points out of these two games at home and we did it so we can go home very happy."
Fabregas, himself, has become a vital performer in Jose Mourinho's side since joining from Barcelona this summer and he already has seven assists to his name.
The 27-year-old has brought creativity to the side and they look an unstoppable force this season.
Chelsea have already opened up a gap of five points over last season's champions Manchester City and it is difficult to see how they will slip up.
They look strong in every department and will now be hoping to build on their impressive opening season form to bring home a long-awaited title to Stamford Bridge.
Their next game is after the international break, in two weeks' time, and they will be looking to extend their unbeaten run in the league to eight games against Crystal Palace.