Winger Pedro scored on his debut as Jose Mourinho's men kick-started their title defence with a 3-2 win at West Brom on Sunday.
He also set up Diego Costa for Chelsea's second just days after arriving from Barcelona for a reported £21million as the visitors survived the second-half dismissal of John Terry.
And Azpilicueta, who scored Chelsea's third at The Hawthorns, believes there is even more to come from his Spain team-mate.
He said: "He has trained for one week, he played his first game, he is discovering the Premier League and I'm sure he will get better.
"I know him very well and he fits into the team very well
I know his ambition, he is hungry to help the team, win trophies and I know the way he started the first game is amazing.
"I know from the national team he is a top player
He played for Barcelona for so many years and he fits into our team and the Premier League."
Pedro joined Baba Rahman at Stamford Bridge last week as Mourinho reacted to Chelsea's sluggish start following a draw with Swansea and defeat at Manchester City.
Left-back Rahman signed from Augsburg and Azpilicueta welcomed the extra competition, having already seen off Ashley Cole and Filipe Luis in his time at Stamford Bridge.
"They are two good additions to the squad, it helps everybody to have competition," said the 25-year-old defender.
"We know in football there's nothing in the past, you have to prove (yourself) every day
We won the league last year but we have to show in every game and training we are ready.
"I am confident to keep working, keep doing my job
I know the competition is good for the team and I had a few great players around me
At the end, hopefully the team will be better."
Victory on Sunday was Chelsea's first of the season, after Thibaut Courtois saved James Morrison's penalty before the midfielder scored twice for the Baggies, and Azpilicueta admitted it was vital.
"It was important to get the win
We had a few difficulties and we had to fight until the end," he said.
Source : PA
Source: PA