Chelsea have collected seven points from three games since the German took over from the dismissed Frank Lampard last month, seeing the Blues rise up to sixth.
Meanwhile, Jose Mourinho’s Tottenham have suffered three consecutive defeats and slide down to eighth on the table.
Jorginho scored the only goal of the game, a 24th minute penalty won by Timo Werner after a needless foul from Eric Dier who was sprawled on the ground at the time of the tackle.
Mourinho said: “The first half wasn’t easy. They were dominating us, they created some imbalance in our left side, it wasn’t easy.
“But the reality is that they scored on that penalty. After that, no problems, no panic, no big chances.
“The game was more in their hands in the first half, but nothing coming out of that. In the second half, completely different.
“We were the best team, we pressed higher, recovered the ball faster, getting more players into attacking areas and in the second half, I believe we deserved more than what we got.”
Despite Mourinho’s assessment, Chelsea had more possession (59-41%), more shots (18-7), better pass accuracy (88-81%) and more corners. Tuchel said the Blues deserved the win.
“In general I am very pleased with the result, it is a deserved win,” Tuchel said.
“We were very good in the first half, very dominant and strong with the ball, good counter-pressing and we did not allow counter-attacks against one of the most dangerous sides.
“We lacked a little bit of precision in the box and composure to make it 2-0 and to score more goals and decide the match, so the second half was a bit hard.”