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Tributes were paid to Jimmy Greaves, Spurs' record goalscorer following a prolific spell with Chelsea, before kick-off at Tottenham Hotspur Stadium after the legendary striker died aged 81.
It was fitting that two clubs Greaves served so magnificently met on the day of his passing – and it was Chelsea who came out on top courtesy of a storming start to the second half.
After Silva headed Thomas Tuchel's side in front, Kante's deflected shot doubled their lead and Rudiger fired home in stoppage time, sending the Blues top of the Premier League, though it is level on 13 points with Liverpool and Manchester United.
Spurs were on top in the opening stages following a rapturous minute's applause for 1966 World Cup winner Greaves, but it was Chelsea who had the first real opportunity.
Tottenham was caught out by a blistering break, but Mason Mount's shot was well blocked by Emerson Royal after the England midfielder had played a one-two with Romelu Lukaku.
The alert Rudiger prevented Sergio Reguilon from picking out Giovani Lo Celso for a tap-in and Son Heung-min's touch let him down when he was played through during an entertaining first half, although the fit-again forward may have been offside.
Kante replaced Mount before the resumption and Chelsea went ahead four minutes after the break, Marcos Alonso whipping in a corner that Silva met with a downward header.
The European champion was dominant, Eric Dier clearing a close-range volley from the unmarked Alonso off the line after Cesar Azpilicueta had picked his fellow wing-back out.
Chelsea doubled its lead in fortunate fashion after 57 minutes, though, with Kante's shot taking a huge deflection off Dier to give Lloris no chance.
Timo Werner wasted a chance to add a third Chelsea goal when he got the ball stuck under his feet after Lukaku slipped him in, before the Germany forward was denied by Lloris amid panic in the Spurs area.
Mateo Kovacic failed to beat Lloris from a tight angle with Spurs on the ropes, but Rudiger did add insult to injury in stoppage time, firing home Werner's pass with his right foot.