Chelsea's Nemanja Matic (R) skips a tackle by Middlesbrough's Marten de Roon during their English Premier League match, at Stamford Bridge in London, on May 8, 2017Chelsea's Nemanja Matic (R) skips a tackle by Middlesbrough's Marten de Roon during their English Premier League match, at Stamford Bridge in London, on May 8, 2017 (AFP Photo/Ian Kington)
Tottenham Hotspur's surprise defeat at West Ham United last week handed Chelsea the initiative and they can now seal a second title triumph in three years if they win at West Bromwich Albion on Friday.
"We're very close. We must be honest. But we need to do another little step and win another game," Conte told reporters after Monday's match, which condemned Middlesbrough to relegation.
"For sure now I'm a bit relaxed. This step was big for us, a big win.
"Now we need to do another step. We have the possibility to do this on Friday against West Brom.
"For sure it won't be easy, because West Brom is a really good team, a physical team, and we must pay great attention.
"We are very close, but we need another step to become champions of the Premier League, which would be a fantastic achievement for us."
While victory at West Brom will deliver the title, Chelsea also have home games against Watford and Sunderland in which to snare the three points they need to make it across the finish line.
Marcos Alonso also found the net in the first half.
Fabregas began the season on the bench after new signing N'Golo Kante took his place, but he has played an increasingly prominent role in recent weeks.
"Cesc is one of the best examples of our season," Conte said.
"Because in this season, Cesc at the start didn't play a lot. And then through hard work, he improved a lot. And then he's playing in every game.
"This development of Cesc is our development, because we started the season with a lot of problems. But through hard work, together we found the right way.
"Cesc is showing (himself) to be a fantastic player and I'm pleased for him. Because I saw in this season that he put himself in this team in every moment, if he played or didn't play. Now he's deserving this."
- Boro 'devastated' -
Needing victory to stand a realistic chance of preserving their top-flight status, Boro succumbed to a defeat that sent them into the Championship alongside northeast rivals Sunderland.
Conte made a point of saluting Boro's travelling fans after the game.
"It's great to see a team that got relegated and to see the fans clapping the players and the players staying there to receive the applause and to clap the fans," said the Italian.
"It's important to celebrate your win, but also to have great respect and clap this type of situation.
"Because I think this situation happens only in England. In Italy it's very, very difficult to see a team getting relegated and the players receive (applause)."
Boro manager Steve Agnew said his dressing room was "devastated".
"We've worked so hard for a number of years to get back into the Premier League and we know how tough the Premier League is," he said. "Obviously we've come up short."
Agnew, who took over in a caretaker capacity after Aitor Karanka was sacked in March, would not be drawn on whether he would like the role on a permanent basis.
"I don't think it's about my situation. It's about the football club," he said.
"We all know it's a Premier League football club in terms of everything about it –- the supporters, the stadium, the training ground. The infrastructure is all there.
"So we have to finish the season strong. We have two games to go. We need to gain more points.
"And then everything moving forward will be towards getting Middlesbrough Football Club back into the Premier League as soon as possible."