Jorginho's first half spot-kick was enough to separate the sides despite a slew of chances to make the scoreline more attractive for the visitors.
A strong start
Chelsea started on the front foot and had a half chance to open the scoring inside the first 11 seconds when Cesar Azpilicueta's lofted ball from deep found the head of Timo Werner in the Spurs penalty area, but the German striker's effort was high and wide.
Callum Hudson-Odoi has enjoyed something of a resurgence under Tuchel, starting all three games since the 47-year-old's appointment and he was influential again here as the visitors attacked primarily down the right-hand side.
Chelsea would have expected to see more of the ball against a Jose Mourinho team, but the question was whether or not they would be able to break them down, something they failed to do in November's 0-0 draw at Stamford Bridge.
In the 23rd minute it was Azpilicueta and Werner linking up once more, down the right side, the former picking out the latter goalside of the Spurs back four.
Eric Dier struggled to clear for the hosts and ended up bringing down Werner, leaving the referee with no choice but to point to the spot.
Jorginho stepped up, despite having missed three penalties this season, and made no mistake planting his effort beyond the dive of Hugo Lloris.
Great buildup with no end product
The front three of Werner, Hudson-Odoi and Mason Mount were linking up really well with Reece James and Marcos Alonso providing good width down the flanks, but for all of Chelsea's silky interplay, they were only able to manage one shot on target following the penalty.
This came from Mount with 15 minutes to play, the 22-year-old combining with Werner and manufacturing the space to hit a low drive across goal on his weaker left foot, but Lloris was equal to it.
The hosts were largely toothless, managing just seven attempts to Chelsea's 18, and as the game wore on they pushed more men forward in search of an equaliser, giving the visitors more space to counterattack.
The blues, however, let themselves down in the final third at times and let Spurs off the hook many times.
The lack of edge almost cost them three minutes from time when Serge Aurier whipped in a fantastic ball from the right flank that Carlos Vinicius headed wide from six yards out.
Tuchel has kept three clean sheets in his first three games in West London, claiming seven points from an available nine.
Chelsea will now turn their attention to the trip to bottom of the table Sheffield United on Sunday evening looking to close the gap on the teams above them, particularly with Liverpool welcoming Manchester City earlier in the day.