A fine first-half Cesc Fabregas goal made it 10 league wins in a row and moved the Blues six points clear at the top of the table.
Fabregas, in for Nemanja Matic, finished off a flowing move a few minutes before the end of a half we dominated. After the break, we were indebted to Thibaut Courtois for two world-class saves that must rank among the very best he has made for the club. The second, to deny Patrick van Aanholt, came in the third minute of stoppage time as we were nearly punished for our profligacy at the other end.
But three more points it was meaning we have equalled our club-record run of consecutive league wins made in the same season. A win at Crystal Palace on Saturday would match our all-time best sequence.
A small knee injury ruled Eden Hazard out so Willian started in his place. Pleasingly, there was a spot on the bench for Kurt Zouma, present in a matchday squad for the first time since sustaining a serious injury in February.
There was a wonderful moment ahead of the game when five-year-old Bradley Lowery, who has cancer and has been given weeks to live, struck a goal past Asmir Begovic to fulfil his dream of scoring for Sunderland at the Stadium of Light.
There was also plenty of applause for Bradley from all sides of the ground five minutes into the game.
Even at that early juncture of the contest it was apparent Chelsea would, as on Sunday, be required to break down a numerous and well-organised rearguard. David Moyes had opted to match our formation, but with two much deeper wing-backs than what we have become accustomed to seeing.
Despite that, the first presentable opening of the evening fell Sunderland’s way, Adnan Januzaj finding space in the box and curling over midway through the half. A minute later, Marcos Alonso superbly picked out Diego Costa but, on the run, he couldn’t control his volley. The former Sunderland man was getting of plenty of joy out on the left.
Jordan Pickford saved magnificently from an offside Pedro and also held on to a deflected David Luiz free-kick. There was nothing the impressive young keeper could do to prevent us taking the lead on 40 minutes, though.
N’Golo Kante leapt high above the significantly taller Jan Kirchhoff to nod a midfield header to Pedro. He slipped it inside to Fabregas who suddenly had space to advance and find Willian. The Brazilian returned it, instead of going alone, allowing Cesc to pick his spot in the bottom right-hand corner for his first league goal of the season.
It was a fine finish, celebrated joyously down below the travelling Blues faithful. In the flash of an eye, we were ahead.
With an edge-of-the-box free-kick Willian then nearly doubled our advantage right on half-time, John O’Shea following Jermaine Defoe into the book for taking down the dangerous Diego Costa.
A controversial moment presented the Mackems with a chance to level 90 seconds into the second period. A Sunderland pass forward hit referee Neil Swarbrick and ran kindly in Defoe’s path. He slipped in Januzaj who drew an outstanding save, with his left foot, from Thibaut Courtois.
At the other end, Moses flashed a drive over and Willian saw a good strike hit former Blue Papy Djilobodji then loop over Pickford and on to the top of the bar. The keeper got down well to deny Diego Costa as the frequency of our efforts on goal increased. Willian, and later the excellent Kante, were the next to have a go.
On the odd occasion there was still defending to be done but the Blues, including Cesar Azpilicueta on his 200th Chelsea appearance, looked solid once again.
Matic for Pedro was Conte’s first change of the night. Moyes had already made two and the introduction of a third, Wahbi Khazri, brought back memories of his wonder goal in the corresponding fixture last term.
Fabregas had a late chance to double his and our tally but volleyed wide.
A brave defensive header from Azpilicueta denied Januzaj a good chance and as we ticked into three minutes of added time, Jason Denayer headed straight at Courtois.
It was nowhere near that easy for our keeper when Van Aanholt let rip from the edge of the box after we failed to clear a high ball. The Dutchman’s well-hit strike looked destined for the back of the net - Van Aanholt was already off celebrating - but somehow Courtois sprang to his right and clawed it out.
‘Thibaut! Thibaut!’ shouted the away end above him, and quite right too. It was a save that single-handedly preserved the points.
Chelsea (3-4-3) Courtois; Azpilicueta, David Luiz, Cahill (c); Moses (Ivanovic 90+3), Kante, Fabregas, Alonso; Willian (Chalobah 89), Diego Costa, Pedro (Matic 75).
Unused subs Begovic, Zouma, Loftus-Cheek, Batshuayi.
Scorer Fabregas 40
Booked Pedro 56, Moses 90+2
Sunderland (3-4-3) Pickford; Kone, O’Shea (c), Djilobodji; Jones (Love 59), Denayer, Kirchhoff (Larsson 57), Van Aanholt; Januzaj, Defoe (c), Borini (Khazri 82).
Unused subs Mannone, Asoro, Maja, Honeyman.
Booked Defoe 43, O’Shea 45+2, Borini 71
Referee Neil Swarbrick
- The full 90 minutes of tonight's match will be available to watch on Chelsea TV from midnight