The Spain international hit before half time to break the Black Cats' resolve, as Antonio Conte's men kept a firm hold on the Premier League summit
Antonio Conte's side took full advantage of Arsenal's 2-1 loss at Everton on Tuesday to secure a firm grip on pole position, Fabregas netting the decisive goal after 40 minutes against a largely toothless Sunderland, although Thibaut Courtois was called upon to make a stunning injury-time save from Patrick van Aanholt to preserve the visitors' advantage.
Chelsea's position contrasts starkly to that which they held exactly one year ago, when a 2-1 defeat away at Leicester City left them one point clear of the relegation zone after 16 matches and proved to be the final game in Jose Mourinho's second stint in charge.
Sunderland were guilty of sitting deep and letting the Blues dictate terms, Fabregas finally making the breakthrough in a tepid first half when he steered a pass from Willian – making his first Premier League start since October 1 with Eden Hazard absent through injury – past Jordan Pickford.
David Moyes' team lacked coherency in attack and, after Adnan Januzaj was denied by Courtois, only the crossbar stopped them slipping further behind to Willian's deflected shot in the 51st minute.
Pickford kept the in-form Diego Costa at bay but Chelsea had done enough to continue their exemplary run of form, while Sunderland remain rooted to the bottom.
Chelsea dominated possession in the first half but struggled to break down a well-organised Sunderland defence, though the hosts were unable to keep hold of the ball when they won it back.
A rare foray forward from Moyes' team ended with Januzaj failing to get enough bend on an 18-yard effort to pick out the top-left corner after 25 minutes.
Chelsea responded with a swift break down the left that saw Marcos Alonso's drilled delivery find Costa, who was unable to cope with the pace on the ball and skewed a volley wide.
Conte's team continued to control proceedings and finally broke through five minutes before half-time when Billy Jones' stray header on the halfway line was pounced upon by N'Golo Kante, enabling Chelsea to surge forward with Willian teeing up Fabregas to guide home from the edge of the box.
Willian was unable to get enough dip on a free-kick from just outside the area in order to test Pickford in first-half stoppage time.
Januzaj was denied by an excellent near-post save from Courtois within two minutes of the restart, but it proved to be a flash in the pan for Sunderland.
Willian's attempt from the right-hand side of the box deflected off ex-Chelsea defender Papy Djilobodji and hit the bar on its way behind, while Pickford got a strong pair of hands down to his left to keep out Costa in the 53rd minute.
Jones was replaced by Donald Love after sustaining an injury in the 59th minute but Sunderland were unable to stem the flow with efforts from Victor Moses and Willian flying wide of the target.
Having spent most of the evening on the back foot, Sunderland almost conjured up an equaliser in the 93rd minute, Courtois springing to his right to palm a swerving effort from former Chelsea man Van Aanholt around the post.