The Portuguese have the distraction of a sensitive opening game against the country's former colony, Angola in Cologne on June 11.
They then face a talented Iran team in Frankfurt before what could be the decisive match against Mexico in Gelsenkirchen.
Mexico are the seeded side in the group and proved they could be a danger in Europe during the Confederations Cup in Germany last year.
Portugal will inevitably carry a measure of self-doubt into the tournament after a first-round exit last time.
That flop highlighted the need for a change and they got it with the appointment of Scolari.
The Brazilian had just led his native country to a fifth World Cup and he then led Portugal to the final of Euro 2004.
"Big Phil" recently turned down the chance to succeed Sven Goran Eriksson as England coach, announcing instead a further two-year extension to run to 2008.
Luis Figo has returned and his last big tournament could be his best chance of success, with Cristiano Ronaldo, Simao Sabrosa and Deco maturing into world class players around him.
But the first round is fraught with dangers, first among them them the clash with Angola, which gained independence from Portugal in 1975 and debuts at the World Cup after a 27-year civil war.
Hopefully the match will be remembered for more positive reasons than the last meeting between the two in 2001, when the game in Lisbon had to be abandoned with Angola down to seven men and 5-1 down with 20 minutes to go.
On the same day Portugal play Angola, another sensitive match will see Mexico play Iran in Nuremberg, the city that become synonymous with the Nazi Rallies.
Iran President Mahmoud Ahmadinejad labelled the Holocaust a myth, raising some calls for the country to be banned from the World Cup.
Mexico have fallen in the second round of the last three World Cups. They impressed everyone as they reached the semi-finals in the Confederations Cup, however, and under gruff coach Ricardo La Volpe they have every reason to be confident.
Iran have won just one match in two appearances in the World Cup finals but they bring a squad packed with talent to Germany, Ali Karimi of Bayern Munich, known as the "Wizard of Tehran", and Hamburg SV's Mehdi Mahdavikia.
