The Spain international's future at Stamford Bridge has been called into question this season due to manager Antonio Conte regularly opting to start the 29-year-old on the substitutes' bench.
Fabregas was named in the first XI for Tuesday night's game, and played a pivotal role by scoring twice in extra time as Chelsea came from 2-0 down to grab a 4-2 victory.
After the match, the midfielder hit out at the media by telling reporters: "I was happy to play from the start. Hopefully this will shut up a few journalists and others who have been speaking rubbish. They should focus on Chelsea winning."
Fabregas's performance could put him in contention for a starting spot in Saturday's Premier League clash against Arsenal at the Emirates.