New signing Romelu Lukaku made a perfect debut in his first game after returning to Chelsea.
Almost exactly eight years after his last appearance for the Blues, the Belgian star striker took the lead in the 2-0 derby win at Arsenal on Sunday after a quarter of an hour.
In addition to Lukaku (15th minute), Reece James (35th) scored a goal for the Champions League winner from West London, who dominated the game at local rivals Arsenal in the north of the city for a long time and earned his second win in the second Premier League game.
Almost another hit
Lukaku almost scored another goal in the closing stages, but Arsenal keeper Bernd Leno steered his well-placed header to the crossbar.
The German national player Timo Werner only came on a short assignment in the final minutes, but was still celebrated with loud chants by the guest fans.
Lukaku had already been under contract with Chelsea from 2011 to 2014, but could not prevail at the time and was awarded several times before he left the club.
This summer he returned to London from Italian champions Inter Milan for around 115 million euros.
Chelsea coach Tuchel, who had complained about the ineffectiveness of his team last season, described the Belgian as "the missing piece of the puzzle".
Only 1-1 for Manchester
Record champions Manchester United have missed a perfect start to the season.
The team of team manager Ole Gunnar Solskjaer did not get more than 1-1 at FC Southampton coached by Ralph Hasenhüttl.
An own goal by United's Fred (30th) put the underdog in the front, and England international Mason Greenwood equalized in the 55th minute after a submission by Paul Pogba.
The English international Jadon Sancho, who was signed by Borussia Dortmund for 85 million euros, was again not in the starting line-up, but was substituted on in the 59th minute.
The Tottenham Hotspur, in which the willing star striker Harry Kane was in the matchday squad for the first time and came on in the 72nd minute, won 1-0 at Wolverhampton Wanderers.
Dele Alli (9th) scored with a penalty.