Three-time champions Germany celebrated their record 100th World Cup match, the most for any country, in style by steamrolling Cristiano Ronaldo-led Portugal who played for nearly an hour with 10 men after defender Pepe was sent off for attempting a head-butt on Mueller in the 37th minute.
Mueller led a brilliant attacking brand of football with goals in the 12th, 45+1 and 78th minutes while defender Mats Hummels scored the other one in the 32nd minute.
The Group G match at Arena Fonte Nova here, however, did not live up to the pre-game hype of a marquee clash with Germany toying with their opponents and then Pepe's dismissal making it worse for Portugal.
Ballon d'Or winner Ronaldo, who made it to Portugal starting line-up after being bothered by a left-knee injury in the build-up, made little impact on the game. He threatened early with a shot from a break that Germany goalkeeper Manuel Neuer could only block. His other significant involvement was a fine free kick late into the match but Neuer was upto the task.
Germany are now joined by United States on top of the so-called Group of Death after the Americans beat Ghana 2-1 at Natal. US thus avenged their defeat against Ghana in the 2010 World Cup in South Africa in the round of 16.
Elsewhere in Curitiba, Nigeria and Iran delivered the first draw of the World Cup on Monday as they ground out a scrappy 0-0 stalemate in their opening match in Group F.

The draw at the Arena da Baixada in the southern Brazilian city of Curitiba followed 12 mostly high scoring and attacking games.
Germany were a class apart from Portugal in their first match of the tournament with their sizzling display of fast and furious football with Chancellor Angela Merkel watching the match.
Coach Joachim Loew deployed three attacking midfielders without a classical striker and used captain Philip Lahm as defensive midfielder instead of his favourite right back position where Jerome Boateng was tasked to try and stop Ronaldo.
The ploy worked with Germany running over their opponents and keeping Ronaldo more or less quiet for most part of the match.
Playing in his 50th for Germany, 24-year-old Mueller opened the scoring after Mario Goetze was pulled down by Joao Pereira in the box, coolly slotting the resultant penalty kick into the right corner of Rui Patricio's goal.
Hummels then rose above Pepe to double Germany's lead with a well-timed header from a corner.
Pepe was sent off in the 37th minute for charging on and apparently head-butting Mueller who went down theatrically after being hit on the face by his rival.
Mueller scored again just before the break, stripping the ball from Bruno Alves and drilling in a low shot. He completed his hat-trick in the 78th minute in a goal-mouth scramble after Portugal goalie Patricio had parried a shot.
In the process, Mueller, who scored five goals in the 2010 finals in South Africa to claim both the Golden Boot and best young player award, scored his 20th international goal and eighth World Cup goal over two editions.
With Monday's win, 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.
In Natal, US got off to a dream start as captain Clint Dempsey scored the opener after just 30 seconds -- the fifth fastest goal in World Cup history -- and German-born John Brooks headed a dramatic winner in the 86th minute.
Andre Ayew equalised for Ghana eight minutes before the end. But Brooks' first goal for his adopted country avenged defeats to the same opposition in the past two World Cups, the latter when Ghana went on to the quarter-finals.

Pepe faces possible three-game ban after red card
Portugal defender Pepe faces the possibility of a three-match ban for violent conduct after being sent off in the first half of Monday's World Cup Group G game against Germany.
Pepe, who has a long history of losing his cool and lashing out at opponents, leant into Germany striker Thomas Mueller with his head, making contact and applying pressure in a needless altercation that could bring him a stiff punishment.
The Brazil-born centre back had caught Mueller in the face in an innocuous-looking challenge but took umbrage as Mueller went down, returning to the forward and thrusting his forehead against the German's.
Serbian referee Milorad Mazic had no hesitation in dismissing Pepe in the 37th minute.
A red card brings a mandatory one-game ban at the World Cup but that is usually extended in the case of a sending-off for violent play.
Pepe's latest episode of violent conduct follows a series of similar incidents in recent years playing for his club Real Madrid, including one in a La Liga match against Getafe in April 2009 which earned him a 10-game ban.
With the scores level at 2-2 and three minutes left in the clash at the Bernabeu, Pepe pushed Getafe's Francisco Casquero and the referee awarded a penalty.
Pepe then kicked Casquero on the ground and a second swipe saw him rake his studs over the midfielder's back. In the ensuing melee he struck another Getafe player, Juan Albin, in the face.
He was shown a straight red card, having already picked up a yellow earlier in the match. He was red-carded in a bad-tempered Champions League semi-final against Barcelona in 2011 for a studs-up lunge on Barca full back Dani Alves and earned wide condemnation for stamping on Lionel Messi's hand in another Real-Barca game in 2012.

Meireles gesture was tactical, not insulting: Portugal
Portugal have denied midfielder Raul Meireles was making an insulting gesture toward the referee after team mate Pepe was sent off against Germany on Monday, saying he was simply passing on tactical instructions from coach Paulo Bento.
Photographs posted on Twitter showed Meireles gesturing with his fingers behind Serbian referee Milorad Mazic's back during the first half of Germany's 4-0 Group G win.
"The Portuguese football federation (FPF) reiterates that there was no gesture directed to the match referee and regrets the speculation which would seriously damage the interests of the player and the national team," they said a statement.
"The FPF clarifies that the gesture, which has been misinterpreted, was directed at team mate Bruno Alves and merely indicated instructions from coach Paulo Bento,” the statement stated,
"Raul Meireles was just explaining that he would drop back to the position of central defender, playing on the right of the defence."
The incident occurred after Portugal defender Pepe was shown the red card in the first half of Monday's game.
Pepe leaned into Germany striker Thomas Mueller with his head, making contact and applying pressure in a needless altercation that could bring him a stiff punishment.   

German media heaps praise on Loew's team               

German media was full of praise on Tuesday for a sterling performance by Joachim Loew's team in their opening 4-0 World Cup win over Portugal that instantly wiped away fears they might have lost their edge.
From the Black Forest in the south to the Baltic Sea in the north, newspapers and commentators expressed awe over the way hat-trick hero Thomas Mueller and his team mates destroyed Portugal - considered their toughest Group G opponents.
"This is going to be our World Cup. Mueller is already talking about winning it all," wrote Germany's best-selling daily Bild newspaper.
Even though German newspapers are usually critical and tend to look for the fly in the ointment, they could find nothing to complain about with the dominant performance against Portugal.
"Mueller destroys Portugal," read the headline in Die Welt.
The conservative Frankfurter Allgemeine Zeitung (FAZ) said "everything went perfectly against Portugal" and added that everything Loew had wanted to happen had happened.
"Everything Loew planned worked out well. Everything he wanted worked -- a lot of variety, quick attacks that originate in midfield and overwhelming the opponent with speed and shifting positions," wrote the FAZ.
The paper said Germany had "made Portugal dizzy with the way they played". It added: "This match was the way Loew wants Germany to play soccer, a style that had only succeeded in brief phases so far this year."

Brilliant Mueller            

The Sueddeutsche Zeitung newspaper in Munich said the only blemish was an injury to defender Mats Hummels.
"Germany opens its tournament with other-worldly strength. The start of the World Cup could not have been any better for the Germany team. Mueller was brilliant with his three goals," wrote the Sueddeutsche.
Berlin's Der Tagesspiegel newspaper said Loew deserved credit for the daunting performance.
"Eins, zwei, drei, vier! Germany beats Portugal 4-0 and Joachim Loew did everything right before the match. The injury to Hummels is the only downside but apparently that's not even as serious as first thought," der Tagesspiegel said.
ARD TV commentator Reinhold Beckmann also got caught up in the euphoria.
"The 4-0 win over Portugal now makes it clear that Germany are among the top favourites to win the tournament alongside Brazil and the Netherlands," said Beckmann.


Latest News from Sports News Desk