A kind draw has left Portugal with an eminently winnable quarter-final against Poland which would be followed by a semi-final against Wales, Hungary or Belgium.
Portugal have already maintained their record of reaching the quarter-finals on all 10 occasions they have taken part at European championships.
Even so, they have been one of the most enigmatic teams at this tournament and their performances so far would not lead them to be considered potential finalists.
Portugal have some of the tournament's most gifted players, including Cristiano Ronaldo, and an attacking philosophy yet all four of their games have been drawn after 90 minutes, two of them goalless.
They are habitually labelled as underachievers despite having reached a European championship final, semi-final and World Cup semi-final in the last 12 years, a remarkably good record for a country with just over 10 million people.
Fernando Santos is one of the tournament's most amiable coaches, yet his team seem to be one of the most unpopular.
Ronaldo, in particular, has been criticised for snubbing Iceland's players at the end of their 1-1 draw, not playing for the team and throwing a reporter's microphone into a lake when he was asked a question during a team walk.
The aggression and theatricals of central defender Pepe have also antagonised neutrals.
Portugal arrived in France on a wave of confidence after thumping Estonia 7-0 in their final warm-up match.
They began the tournament by taking an early lead against Iceland but lost concentration, conceded a sloppy equaliser and then lacked the inspiration to break down the Icelandic wall for a second time.
They then dominated Austria but were held 0-0 with Ronaldo missing a penalty. Needing a point against Hungary, they had to come from behind three times to force a 3-3 draw.
Against Croatia on Saturday, they played for nearly two hours without managing a shot on goal in a dire match before Ricardo Quaresma, himself a player who blows hot and cold, headed in a dramatic winner.
When Santos recently suggested that he would return to Portugal on the day after the final and be welcomed with a party, his comments were greeted with incredulity.
Suddenly that looks like a distinct possibility and Portugal could do it even without playing to their full potential or endearing themselves to the neutrals.
(Writing by Brian Homewood in Nice; editing by Clare Fallon)
