Müller's haul overshadowed World Player of the Year Cristiano Ronaldo, who suffered his fourth straight defeat against Germany in the key Group G clash.
The 24-year-old Müller made his breakthrough at the 2010 World Cup when he finished as joint top-scorer with five goals in South Africa to win both the Golden Boot and young player award.
Four years on, he converted a first-half penalty against Portugal, then fired home his second to give Germany a 3-0 half-time lead before wrapping up his hat-trick with a scrappy third in the closing stages.
"That doesn't happen everyday, but I have had a good run at World Cups and I wanted to pick up where I left off," he said after picking up the man-of-the-match award.
"I am known for giving my utmost, but no one could have assumed that would happen and I can't say that will happen again in the next match, but I'll certainly try."
Normally a winger or attacking midfielder for Bayern Munich, Müller was given a rare start as striker, keeping veteran Miroslav Klose, 36, on the bench.
With eight World Cup goals now to his credit, Müller is rapidly approaching Klose's joint German record of 14 World Cup goals, shared with 1970s legend Gerd Müller.
But he insists winning the World Cup is his top priority when asked if he wanted to claim ex-Brazil star Ronaldo's all-time record of 15 goals at World Cup finals.
"Let's remain objective here, this was just the first match," he said.
"We just want to be world champions and if we do that, records may or may not come, but we have other things to focus on."
After the Netherlands' 5-1 hammering of holders Spain on Friday, the Germans threw down another strong World Cup marker at the same Arena Forte Nova stadium.
"We made a good start and the entire 90 minutes went well for us, we took our chances well," said Müller.
"The second was a set-piece goal which gave us a comfortable margin and even though the match wasn't over, we knew Portugal had an uphill struggle."
Müller was involved in a first-half fracas with Portugal's centre-back Pepe which saw the Real Madrid defender sent off for head-butting the German.
"Things went fast on the pitch, his arm struck me in the face and I'm not sure what happened after that," said Müller.
"I remember his head coming towards me, but things were vague after that.
"I didn't want to provoke it, but anyway, his actions were superfluous."
Germany now face Ghana on June 21st before playing the USA on June 26th when Stars and Stripes head coach Jürgen Klinsmann takes on his former side.
"It was a good start, but we need to focus on the next match now – there are no gifts in football," added Müller.
The Chancellor and I
Arsenal's Lukas Podolski delivered on his pre-match promise to get a dressing room photograph with Chancellor Angela Merkel who flew to Brazil to watch the game.
The German leader visited the team dressing room to congratulate Joachim Löw's side
And Podolski later posted on Twitter: "4-0 win, awesome start! And here the promised Selfie with the chancellor."
Her press spokesman Steffan Seibert later posted a picture on Twitter of Merkel with the entire team. "Congratulations – a perfect start to the tournament!" he Tweeted.
Löw said Merkel's visit had capped a great day for Germany.
"She gave a little speech to say now nice it was that we won, especially after such a long trip here," said Löw. "There was a lot of applause. We always like it when she comes to see us, she is always a nice guest to have."