Chelsea manager Jose Mourinho praised Pedro's instant impact after the winger scored on his debut in the 3-2 win over West Bromwich Albion.
Pedro also set up Diego Costa for Chelsea's second before Cesar Azpilicueta's goal and they hung on after John Terry's second-half dismissal on Sunday.
The Spain star only joined Chelsea from Barcelona last week and Mourinho believes the 28-year-old has proved he can handle the Premier League.
He said: "He's a very good player. There is always a question mark because how many top players come to England and don't perform immediately?
"People ask if he is the right player, can he adapt? We have examples in our club and there are lots of examples in other clubs, it's very nice for him to perform the way he did."
Cesc Fabregas, who played alongside Pedro at Barca, told the club's official website: "He was fantastic. I knew straight away he would make an impact because it was something we didn't have in our team -- a player who goes behind defenders, that goes one against one, and stretches the team.
"The mentality of this guy is fantastic and I'm very happy for him."
Pedro, who had spent his entire professional career at the Camp Nou, added: "I enjoyed my debut with this team a lot.
"It was important for me [to score] for my adaption in the team and I'm really very happy for the victory."