The Blues pipped Crystal Palace 3-1 at Selhurst Park after being more clinical in front of goal in what was a very even match on paper.
Chelsea produced fewer shots but more xG as the sides traded chances in an end-to-end game that was all action for the full 90 minutes.
The visitors' superior cutting edge in front of goal proved to be the difference and went ahead in the 34th minute when Estavao jumped on a poor attempted back pass from Jaydee Canvot before blasting the ball past Dean Henderson.
They doubled their advantage five minutes after the break when Estevao played Joao Pedro through with a lovely chipped pass and the Brazilian showed great skill to beat Adam Wharton before firing past Henderson.
Enzo Fernandez secured the win with a well-taken penalty in the 64th minute after Canvot handled the ball in the box.
Palace's afternoon got even more difficult in the 72nd minute when Wharton was sent off after being shown a second yellow card, but they did manage to get a late consolation goal from Chris Richards in the 88th minute to salvage a bit of pride.
Up north at St James' Park, Villa stunned Newcastle United 2-0 despite being up against it for large periods of the match.
Newcastle produced more shots and more than twice the xG of Villa but could not find a way past Emiliano Martínez in the visitors' goal.
It was the Villains' first win in Newcastle since 2005 and cemented their hold on third place in the Premier League, while drawing level on points with Man City in second.
Emiliano Buendia opened the scoring against the run of play for the visitors with a beautiful curling effort into the top corner.
Newcastle pushed for an equaliser all game but were thwarted time and again before Ollie Watkins put Aston Villa out of sight when he nodded home from close range in the 88th minute to put the visitors into an unassailable 2-0 lead.
Michael Carrick put a dent in Arsenal's Premier League title hopes with a dramatic 3–2 win, claiming maximum points from his first two games in charge of the club.
Pep Guardiola aimed strong criticism at match officials after Manchester City's 2-0 win over Wolves, despite the result ending a four-game winless league run and cutting Arsenal's lead at the top to four points.
Liverpool manager Arne Slot has suggested that some players 'ran out of energy' in the final minutes of the 3-2 defeat against Bournemouth at the Vitality Stadium on Saturday.
Lyle Foster came off the bench to score as Burnley drew 2-2 against Tottenham Hotspur while Manchester City were back to winning ways in the Premier League after a 2-0 success over Wolves.
