The 23-year-old Brazilian forward, signed from Brighton and Hove Albion for 60 million pounds (about $A125 million) last week, curled home a fabulous strike in the 18th minute on Tuesday (Wednesday AEST), before sealing the win with a brilliant finish following a counter-attack early in the second half.
Chelsea will face Real Madrid or Paris St Germain, who meet in the second semi-final on Wednesday (Thursday 5am AEST), in Sunday's final.
"I'm pleased about everything, to be honest. It's a great achievement," Chelsea manager Enzo Maresca told DAZN.
"It's been a fantastic season. To finish top four in the Premier League, win the Conference League title, now in the final in the Club World Cup. We are so, so, so happy.
"We knew with Joao Pedro that we have a player that is able to do what he has just done."
The striker himself was naturally thrilled with the result, but empathised with the South American side.
"I think it was a dream. I don't think it could have been better - two goals. Now we need to think about the final,'' Pedro said.
"I am happy to score my first goals for Chelsea, but also I know this tournament is very important for Fluminense.
"I can just say sorry, but I have to be professional. I play for Chelsea. They pay me to score goals and today I was happy to score.
"Now I need to rest, focus on the final because I think it will be a very important game."
The semi-final took place in brutal conditions in New Jersey, with an afternoon kickoff in scorching heat that prompted a National Weather Service warning. Temperatures soared past 35C, with more than 54 per cent humidity.
Chelsea started the game in control against a Fluminense side who adopted a conservative approach, with a deep five-men defence, inviting their rivals to hold possession and trying to counter-attack.
The English side struggled to find their way through against Fluminense's defensive block, but broke the deadlock in the 18th minute thanks to Pedro's shot from the edge of the box into the top corner of the net.
The Brazilian refused to celebrate his goal, a gesture of respect for Fluminense, where he came through the academy before making his professional debut as a 17-year-old. His journey took him to Watford in 2019 and Brighton in 2023, before joining Chelsea.
Fluminense, who stunned Champions League runners-up Inter Milan in the last 16 and Al-Hilal in the quarter-finals, nearly equalised when Hercules burst unmarked into the box following a slick one-two with German Cano, only for Marc Cucurella's goal-line clearance to preserve Chelsea's lead.
The Brazilian side thought they had earned a lifeline when referee Francois Letexier awarded a penalty for Trevoh Chalobah's handball, but VAR overturned the decision.
Just as Fluminense appeared to be building momentum in the second half, Pedro delivered the knockout blow in the 56th minute.
He took a fine pass by Enzo Fernandez, before dribbling past Ignacio and smashing in an unstoppable shot off the underside of the crossbar.Â
- with PA
