Pedro Rodriguez enjoyed a Chelsea debut to remember but John Terry was sent off as Jose Mourinho's side beat West Bromwich Albion 3-2 for their first Premier League win of the season.
Pedro, who signed from Barcelona this week, scored and grabbed an assist at The Hawthorns as Chelsea bounced back from their 3-0 loss to Manchester City last week.
Goalkeeper Thibaut Courtois was Chelsea's hero on 14 minutes when he saved James Morrison's penalty kick with his legs after Nemanja Matic had brought down Callum McManaman in the area.
Chelsea broke the deadlock on 20 minutes through debutant Pedro, who played a one-two with Eden Hazard before seeing his shot deflected into the bottom corner.
Diego Costa doubled Chelsea's lead 10 minutes later as he got on the end of Pedro's low delivery to slide in from close range.
Morrison then made amends for his penalty miss, powering in from a central position via Salomon Rondon's assist on his West Brom debut.
The Blues restored their two-goal advantage before half-time when Cesar Azpilicueta pounced on a chest down by Costa to guide past goalkeeper Boaz Myhill.
After being substituted at half-time in the defeat at City last Sunday, Terry was sent off early in the second half at West Brom after pulling down Rondon.
Morrison grabbed his second of the game when McManaman whipped a cross in and the Scotland international headed in off the crossbar, but Tony Pulis' side could not find a leveller as Chelsea held on.
Manchester City maintained their 100 percent start to the season as they beat Everton 2-0 at Goodison Park.
Aleksandar Kolarov and Samir Nasri were on target to make it three wins from as many games for Manuel Pellegrini's men, who are top of the Premier League table.
City started very brightly with striker Aguero causing Everton's defence problems only for the Argentina international to twice be denied by goalkeeper Tim Howard.
Everton grew into the first half and on 24 minutes they had the ball in the back of the net only for Romelu Lukaku to be flagged for offside.
David Silva was pulling the strings but City were unable to find a breakthrough before half-time, with Everton going the closest as Lukaku's free kick clipped the top of the crossbar.
Silva continued to be at the heart of things for the away side and early in the second half the Spain international was denied by the post.
City found the breakthrough on 60 minutes through left-back Aleksandar Kolarov, who squeezed a shot in at Howard's near post after receiving Raheem Sterling's pass.
Everton pressed for a leveller but it was not to be as Gareth Barry saw a late effort hooked off the line by City captain Vincent Kompany.
And City wrapped up their victory with two minutes of normal time remaining when Samir Nasri played a one-two with Yaya Toure before lifting the ball over Howard.
In Sunday's other Premier League match, Watford and Southampton played out a goalless draw at Vicarage Road.
Neither side had the cutting edge to find a breakthrough, as Southampton saw Manchester United target Sadio Mane go off injured in the first half.
Ronald Koeman's Southampton are without a win in their opening three matches this season.