Chelsea struggled to create clear-cut chances and required two superb saves from Thibaut Courtois to preventSunderland from equalising.
While they controlled much of the match, Chelsea struggled to create clear-cut chances and required two superb saves from goalkeeper Thibaut Courtois to prevent bottom club Sunderland from equalising.
It meant Chelsea could never relax before extending their winning run to 10 league games, but this was also evidence Conte has created a team that know how to win when not at their best.
The perception that the Chelsea manager can do no wrong only increased when they went ahead five minutes before the interval through a goal created and scored by the two players he called up for this game.
Fabregas, chosen in midfield ahead of Nemanja Matic, was the scorer with a crisp 20-yard shot after he exchanged passed with Willian, who was involved after a long absence because of an injury to Eden Hazard.
The goal gave Chelsea an interval lead that had appeared unlikely for much of a low-key half.
Sunderland provided stubborn resistance while creating only one threat when Adnan Januzaj curled a shot wide in the 25th minute.
Otherwise, Chelsea were the more dangerous side, although it appeared they might miss Hazard's influence as they lacked their usual fluency in the final third.
It took them 26 minutes to carve out their first chance when Diego Costa miskicked as he attempted to volley in a cross.
It was an indication, however, that Chelsea were getting into their stride.
Eight minutes later, Sunderland's defence was opened up before Pedro Rodriguez strayed inches offside when he unleashed a shot that was well saved by goalkeeper Jordan Pickford.
Pickford also saved a free-kick from David Luiz before he was beaten by Fabregas, leaving Sunderland with a solitary clean sheet in their last 17 Premier League games.
There could have been another Chelsea goal in the dying seconds of the half when Willian's free-kick shaved a post.
Sunderland would have been justified in fearing the worst against a Chelsea team who had kept nine clean sheets in their previous 10 games.
But they almost found a way past Courtois only 82 seconds into the second half.
Jermain Defoe created the opening with a pass to Januzaj, whose low shot was turned wide by Courtois's outstretched left leg.
It was a warning that brought a swift response from Chelsea, starting with a shot from Victor Moses in the 47th minute.
Inside the next 10 minutes, Willian hit the bar with a shot that deflected off a defender and Costa was thwarted by Pickford and then an excellent challenge by defender Lamine Kone.
Chelsea's failure to create a second goal that would surely have been decisive meant they had to endure an anxious climax to a game that they had started as overwhelming favourites.
They were pinned back for the last 15 minutes and Sunderland's pressure almost produced a stoppage-time goal when Courtois brilliantly turned away a shot from Chelsea old boy Patrick van Aanholt.