A decisive first-half saw Germany race into 3-0 lead as Müller converted a penalty, then fired home their third on the stroke of half-time after a Mats Hummels header had also hit the target.
Portugal played almost an hour with a man down after defender Pepe was red-carded for aiming a head-butt at Müller.
World Player of the Year Ronaldo played the full 90 minutes of the Group G opener despite recent injuries, but the Portugal captain was powerless to prevent his side being over-run.
The Portuguese suffered the same fate at Salvador's Arena Fonte Nova as their Iberian neighbours Spain last Friday when the holders were routed 5-1 by the Dutch.
Germany continued their domination of Portugal by adding Brazil 2014 to their list of recent wins over Ronaldo's side which includes the 2006 World Cup, plus the 2008 and 2012 European championships.
The result capped a remarkable day for Germany, in front of Chancellor Angela Merkel, just hours after news broke that ex-Formula One champion Michael Schumacher has come out of his lengthy coma.
Having declared himself '100 percent fit', Ronaldo lived up to his word with an early shot, then put Hugo Almeida into space, but the Germans were soon on top.
Sami Khedira fired wide after a loose pass from Rui Patricio with eight minutes gone at the start of a busy period for the Portugal goalkeeper.
When left-back Joao Pereira tugged back on Mario Götze's shirt, Serbian referee Milorad Mazic pointed straight to the spot.
Müller, who scored five goals in the 2010 finals to claim both the Golden Boot and best young player award, planted his penalty in the bottom corner to open the German's account on 12 minutes.
Portugal coach Paulo Bento was forced into an early substitution as Almeida pulled up with a muscle injury to make way for Eder.
Götze then crashed a shot just wide of the post, just before the Germans went 2-0 up.
Toni Kroos swung in a corner and centre-back Hummels out-jumped Pepe to plant his header past Patricio on 32 minutes.
Portugal's fortunes went from bad to worse on 37 minutes when the standing Pepe aimed a head-butt at the seated Mueller after an altercation to earn a straight red card.
Müller had his revenge on the stroke of half-time when he chested down Kroos' long pass and smashed his shot past Patricio as it finished 3-0 at the interval.
After the break, Portugal kept chipping away at the solid German defence, which had been a concern coming into Brazil.
But Portugal's fortunes were summed up when one of Ronaldo's trademark free-kicks cannoned off the German wall leaving the world's best player with his head in his hands.
Having already lost injured midfielders Marco Reus and Lars Bender before arriving in Brazil, there were worrying scenes for Germany coach Joachim Löw when Hummels had to be helped off on 73 minutes.
Sampdoria's 22-year-old Shkodran Mustafi, the son of Albanian immigrants, came on to win only his second cap.
Müller wrapped up his hat-trick on 78 minutes in scrappy fashion in a goal-mouth scramble after Patricio had parried a shot.