The Blues duo, who joined for a combined £60m this summer, made a swift impact as Jose Mourinho's men started their Premier League campaign with a 3-1 win at Burnley.
Costa quickly opened his account, cancelling out Scott Arfield's opener for Burnley, while Fabregas cleverly created the second goal for Schurrle before Branislav Ivanovic completed the scoring.
Asked if the pair will give Chelsea an edge over their rivals, the German forward said: "Yes, I hope so. It was very good.
"I think for Diego it was a perfect start. For a striker to come in and score his first goal is always important. He played fantastic in the friendly, and he scored. And now his first goal in competition.
"Cesc was fantastic for me as well, he always had control of the game. He was always running; two assists. So it was a fantastic night for them both, but it was only the first match and we have to keep going."
Fabregas, named man-of-the-match at Turf Moor, was linked with Manchester United and former club Arsenal before he moved from Barcelona to Stamford Bridge.
"I think a player like Cesc, every team wants him," said Schurrle. "So we are happy that he decided for Chelsea. We are happy that he is a Blue now. I am 100 per cent sure he will help us this season."
In another change to the Chelsea line-up, Mourinho opted for Belgian goalkeeper Thibaut Courtois instead of long-term No.1 Petr Cech.
Mourinho wants Cech to stay and fight for a starting role and Schurrle insists he still has an important part to play this season.
He said: "I hope he stays of course. He is a great character and is very important for the team. He is a fantastic keeper, one of the best.
"It's his decision what he wants to do, but everyone wants him to stay and with him we have a better squad. We will need everyone because hopefully we will have 50-60 matches in all competitions."