A first-half inch-perfect Cesc Fabregas goal helped Chelsea extend their lead to six points at the top of the Premier League table, and secure their tenth win in a row.
The Blues controlled the majority of the possession however they struggled to break down a packed Sunderland defence.
The first 45 minutes saw little created from either side on a wet and cold night in the North East.
A couple of speculative long-range free-kicks from David Luiz, and a poor finish from a good run by Black Cats' Adnan Januzaj were the only highlights from the first 40 minutes.
But it was on that mark that Sunderland's defiant defence was finally broken.
They had done well until then limiting the visitors to just one shot on target, but a perfectly placed Fabregas shot gave the Blues a 1-0 lead.
The Spain international played a simple one-two with Willian before guiding the ball into the bottom right-hand corner from the edge of the area past a helpless Jordan Pickford.
Sunderland started the brightest in the second-half and could have been level, but for an excellent low save from Thibaut Courtois one-on-one against Januzaj.
Shortly afterwards the home side were nearly cruelly punished when a long-shot from Willian cannoned off the dangling leg of Papy Djilobodji and went out for a corner off the crossbar, after looping over stranded Pickford.
Sunderland came extremely close to an injury-time equaliser when Patrick van Aanholt got his shot away through a scrambled penalty area, but Courtois came to the London club's rescue once again with a wonder-save.
Chelsea now sit with a six point gap at the top of the table, but boss Antonio Conte will be hoping their performances improve in games to come,as for the second match in a row they struggled to break-down the opposition.
One positive for the North East side is that Fabio Borini managed to last over 80 minutes on his return from a long-term injury.
However, a worrying sign for David Moyes is Billy Jones - who had to be substituted in the second-half after hobbling off.
Sunderland will have to now pick themselves back up ahead of the weekend when the face the visit of Watford, whereas