The Blues stretched their lead at the top of the table to three points after a 3-0 win at Newcastle United thanks to a brace from Reece James and Jorginho’s penalty.
On the same day, Liverpool threw away a two-goal lead to draw 2-2 at home to Brighton and Hove Albion while Manchester City lost a home 2-0 to Crystal Palace.
Chelsea were missing the services of Romelu Lukaku, Timo Werner, Mason Mount, Cesar Azpilicueta and Mateo Kovacic, and they had to wait until the 65th minute to break the deadlock.
Tuchel’s side now enjoy a three-point cushion over second placed Liverpool while a five-point buffer has been opened over champions Manchester City.
The former Borussia Dortmund and Paris Saint Germain manager is however aware that things can change at the top in a twinkle of an eye in the Premier League and is not getting carried away by their rivals slipping up.
"It's not a moment where we celebrate results on the other pitches," he said. "It's too early and we want to focus on ourselves.
"What goes around comes around. There is a long way to go and if you think I'm even happier now, this is not true.
"We need to keep our feet on the ground. I am happy with the team effort today, but we don't celebrate other teams' results.
"You can lose in this league any match at any minute. So we focus on us and keep going. Let's see where it goes, but it's a long way."
Chelsea will host Burnley in their next league game.
