The Blues consolidated fourth spot on the league log thanks to another dominant performance at Stamford Bridge.
Kai Havertz made decisive contributions in either half as Chelsea remained unbeaten under Tuchel.
The hosts took the lead on 31 minutes when Havertz’s shot took a ricochet off defender Ben Godfrey to beat Jordan Pickford.
Chelsea’s advantage was doubled when Havertz was brought down inside the area by Pickford, with Jorginho slotting home the resulting penalty.
"We deserved to win. It was a very difficult first half but we controlled it completely. Second half we increased our level and had a lot of dangerous attacks,” the former Borussia Dortmund and Paris Saint-Germain coach told BT Sport after the game.
"Very pleased with Kai. It was the trust we gave him and used the trust we gave him. He is a player who has all the ability to be a dominant figure in the offensive part and he stepped up.
"You see the quality of the players and the club. It is a pleasure to be on the sideline and work with the team. Everybody in the club is doing everything to compete at this level."
Next up for Chelsea is a trip to Elland Road to face Leeds United in the Premier League before a crucial game against Atletico Madrid in the second leg of the Champions League Round 16.
