Goals from Diego Costa, Marcos Alonso and Nemanja Matic helped the Blues to secure a comfortable win to move them within a victory of the Premier League title – while confirming the relegation of Steve Agnew's side to the Championship.
Fabregas did not score but nevertheless enjoyed an outstanding performance in the middle of the park, setting up the opener for Costa and the third for Serbian midfielder, Matic.
The former Barcelona and Arsenal midfielder had a difficult start to life under Conte but has managed to turn around the situation during the second part of the season.
His assist for Costa's goal was his 10th of the campaign and helped him to become the first footballer ever to reach that figure in six different Premier League seasons.
"Cesc is one of the best examples of our season. This season he didn't play a lot at the start. Then, through hard work, he improved a lot and now he is playing in every game. This development of Cesc is our development," Conte admmited in the press conference following the victory over Middlesbrough.
"We started the season not in the right way, with a lot of problems, and only through hard work and finding the right solutions together have we found the right way. I think Cesc is showing he is a fantastic player and I'm pleased for him. I saw this season he put himself in this team in every moment if he played, or if he didn't play. Now he is deserving this."
Meanwhile, the victory means that Chelsea only need one more win from their last three games to clinch the Premier League title and the Italian boss urged his players to take that final step in Friday's trip to West Bromwich Albion.
"My message was we need another step, in this part of the season we always right to look at yourselves, don't wait for the other teams. We have a good chance to finish on Friday and become champions. It won't be easy, we have three chances to become champions, we are very close but need another step to become champions of the Premier League, which would be a fantastic achievement," Conte added.
"For sure now I am a bit relaxed. This step was big. It was a big win at this stage of the season. It's great. Now we need to do another step. We have the possibility to do this on Friday against West Brom, but for sure it won't be easy because West Brom are a really good, physical team so we must pay attention,
"But for sure today we took a big step. I must be honest, and I must be pleased for the performance, the commitment, the desire and the will of my players on the pitch. It's great to score three goals, to create many chances and also to keep another clean sheet. I'm satisfied."