Chelsea controlled the early proceedings and Jorginho fired them ahead from the spot on 24 minutes, after Timo Werner had drawn a foul from Eric Dier.
After half-time, Chelsea continued to dominate as Callum Hudson-Odoi flashed a shot wide, Marcos Alonso volleyed over and Mason Mount’s strike was well saved by Hugo Lloris.
However, Spurs threw caution to the wind late on and Carlos Vinicius, on his first Premier League start, headed an inviting cross from Serge Aurier wide.
Dier then narrowly missed the target with a free-kick as Spurs failed to find a way through.
A second successive win moves Chelsea up to sixth on 36 points.
Following a third consecutive defeat Spurs lie two places back with 33.