After managing no shots on target in the first half, the visitors looked like a different team after the break and scored three second-half goals at the Tottenham Hotspur Stadium.
The Blues opened the scoring four minutes after the re-start, when Thiago Silva headed past Hugo Lloris from Marcos Alonso’s corner.
Half-time substitute N’Golo Kante added a second with his first goal in 49 league appearances, though his long-range effort took a massive deflection from Eric Dier.
Antonio Rudiger found the bottom corner in injury time to complete the win.
Spurs started the game brightly and were the better side in the first half, but Nuno Espirito Santo’s side managed just two shots on target throughout and struggled to find a response after going behind.
Silva, Alonso, Rudiger, Romelu Lukaku and Timo Werner all came close as the Blues enjoyed 10 second-half shots on target, but Lloris made a number of saves to deny them.
Chelsea are one of only three teams yet to lose in the Premier League this season, along with Liverpool and Manchester United.
The victory lifts the Blues to joint top of the table, alongside Jurgen Klopp’s side.
Before the game, tributes were paid to Jimmy Greaves who played for both clubs, after he died aged 81.