Harry Kane thought he had given Spurs the lead shortly before half-time when he turned and swept home Steven Bergwijn’s cross. But referee Paul Tierney spotted a push from Kane on Silva in the build-up and disallowed the goal.
Chelsea then found the opener less than two minutes into the second half when Ziyech cut inside before picking out the top corner from 25 yards out with a sensational left-footed strike.
And it was 2-0 before the hour mark when Silva glanced home a header to seal all three points for the home side.
Here are the player ratings from Stamford Bridge.
Kepa Arrizabalaga, 7. Had nothing to do in the first half. Was beaten by Kane before the goal was disallowed. Made a good stop to deny Kane’s header late on.
Cesar Azpilicueta, 6. Spurs failed to really probe down Chelsea’s right-hand side but the one time they did Sessegnon breezed past Azpilicueta, only to skew his attempt well wide. Like the rest of the team, he was far more assured in the second half.
Thiago Silva, 6. Had to walk a tightrope after being booked for a professional foul on Bergwijn midway through the first half. Then looked all at sea up against Kane and was remarkably fortunate to see the England captain’s goal disallowed for a tame push on the Brazilian. Recovered his composure in the second half and netted an important second goal for the hosts.
Antonio Rudiger, 8. Has now played four matches against Spurs this season and barely put a foot wrong in any of them. With and without the ball he is a superb defender. Chelsea need to sort out his contract situation as soon as possible.
Malang Sarr, 7. Very composed for such a young defender. Beginning to look like a staple of Chelsea’s back three amid uncertainty over the future of Christensen.
Jorginho, 6. Kept things ticking over for Chelsea, as always. Not his most impactful game but did enough to limit Spurs’ control of the midfield.
Mateo Kovacic, 7. Cut out a number of Spurs attacks at key times and got Chelsea back on the front foot. Defensively faultless but did not have as much of an attacking influence as he would have liked.
Mason Mount, 8. Spurs struggled to pick him up when he floated out to the right and began linking up with Ziyech. Was clearly the man Chelsea were looking to in the final third but had little help in the form of runners into the box. Went close with a long-range effort in the second half.
Hakim Ziyech, 8. Looked very lively in the opening 20 minutes as he found space in between Davies and Sanchez down the right channel. His delivery was superb throughout but no Chelsea player made it count. Then decided to do it himself and produced a sensational strike to break the deadlock. Nearly scored a second but for a great save from Lloris.
Callum Hudson-Odoi, 5. Struggled to make an impact on the match as Tanganga and Doherty often doubled up on him.
Romelu Lukaku, 6. Had two good chances in the first half - one which he blazed over the top and the other which he failed to connect with altogether. Grew into the game and turned Sanchez with ease in the second period but his shot was routine for Lloris. Linked play well in the latter stages.
Subs: N’Golo Kante (6).
Hugo Lloris, 6. Made a routine stop from Ziyech in the first half. Could do nothing about either of the goals.
Japhet Tanganga, 5. Looked solid for the opening 30 minutes but was then caught napping by Hudson-Odoi and received a booking for pulling him back. Narrowly avoided a second yellow just before half-time. Most of Chelsea’s joy came down his side.
Davinson Sanchez, 5. Appeared a bit more assured next to Dier, although remains suspect with the ball at his feet. Was rolled all too easily by Lukaku and still looks to be lacking something when it comes to his physical presence.
Eric Dier, 7. Missed the last two Premier League games and showed why he could be key to Conte’s plans. Defensively solid and can carry the ball out from the back. Got the better of Lukaku in a number of duels but then gave away the free-kick which led to the second goal.
Ben Davies, 5. Was overwhelmed by Ziyech and Mount drifting between the centre and the right. The game seemed to pass him by.
Matt Doherty, 5. A little fortunate to escape a sending off for a reckless challenge on Sarr in the opening 20 minutes (was not even booked for the tackle). Clearly not comfortable on the right of midfield in a 4-4-2 formation.
Pierre-Emile Hojbjerg, 6. A typically combative performance from the feisty Dane. Was caught out of position a couple of times but enjoyed a fascinating battle with Mount.
Harry Winks, 6. Was tasked with the unenviable job of battling Jorginho and Kovacic in the middle of the park, but showed the grit and technical ability to compete in difficult circumstances. The system did not help him.
Ryan Sessegnon, 4. Found a way in behind the Chelsea defence but fluffed his lines with an awful cross-shot. Offered Davies little support defensively. Was hooked before the hour mark.
Steven Bergwijn, 6. Worked incredibly hard to chase down loose balls and relieve some pressure from his side’s defence. Had very little impact in the second half.
Harry Kane, 7. Dropped deep to link the play between the midfield and Bergwijn. Seemed to enjoy having someone running beyond him. Scored in the first half but was penalised for a soft push on Silva. Went close with a header late on but Kepa saved well.
Subs: Lucas Moura (6), Oliver Skipp (6). Bryan Gil (N/A).