The 24-year-old came off the bench after the interval and struck three times in just nine minutes, leaving Chelsea's new manager impressed by his clinical display.
Alonso revealed Pedro had been highly motivated in training, suggesting the forward's omission from Brazil's World Cup squad had only increased his hunger.
"He's very hungry - Joao is really, really determined to have a great season," said Alonso.
"After a great last year where he scored many goals, I think that he wants to keep scoring more and more. But we need to help him, as on his own it's not possible.
"He will have the players around him and they need to have this hunger to score as well. It's not just about the striker, but every time that we win and our striker scores, I am happy."
Pedro joined Chelsea from Brighton a year ago and enjoyed an outstanding debut season, scoring 20 goals in all competitions. His performances also earned him the club's Player of the Season award, as voted for by Chelsea supporters.
The striker has since said he feels liberated playing under Alonso, who is aiming to restore Chelsea to the top after the club's 10th-place league finish last season.
Despite reports that Chelsea are preparing to offload several attacking players following the arrival of Morgan Rogers from Aston Villa, Pedro is expected to remain an important figure in Alonso's plans.