Iranian defender Sohrab Bakhtiarizadeh put an end to Angola's hopes of progressing to the second round of the World Cup finals with a header 15 minutes from time and secured his side a 1-1 draw in Leipzig.
Needing a victory plus a Mexico defeat to make it through to the last 16 on their debut appearance at the finals, Luis Oliveira Goncalves' side weathered a first-half storm before taking the lead on the hour mark through Amado Flavio with a perfectly placed header.
But, after dominating the opening period without converting a single chance, the Iranians finally found the back of the net when central defender Bakhtiarizadeh - in the starting line-up following a shoulder injury to Yahya Golmohammadi - met Mehdi Mahdavikia's 75th minute corner to earn Iran their only point of the 2006 finals.
The Iranians should, however, have been comfortably in front when the half-time whistle sounded, so dominant was Branko Ivankovic's side.
Joao Ricardo was the busier of the two goalkeepers and he did well to deny the Iran in the 14th minute when Vahid Hashemian's through-ball on the turn put Ferydoon Zandi in on goal, only for his shot to parried to safety.
In the meantime, Ali Daei's desperate search for a World Cup goal continued.
Despite his status as the scorer of the most international goals ever, the veteran forward - expected to retire after this game - has yet to score in the sport's greatest competition.
Against a porous Angolan back line, though, he had the chances to break his duck.
Daei's free-kick from 25 yards out made it beyond the Angolan defensive wall only for Joao Ricardo to punch clear in the 23rd minute and less than a minute later an inch-perfect cross from Mahdavikia found the former Bayern Munich striker in space, but rather than finding the back of the net Daei could only head high and wide.
Angolan midfielder Antonio Mendonca was perfectly placed on the post to clear Zandi's powerful header in the 27th minute and, with five minutes left in the half, Andranik Teymourian's low shot was collected at the second attempt by Joao Ricardo.
The Angolans presented little threat beyond the occasional speculative shot. Mateus sent his first-time effort over the bar in the 12th minute while Fabrice Akwa was also woefully off target just before the half hour.
Ebrahim Mirzapour finally had to make a save of significance three minutes into first half injury time when he pushed Arsenio Love's shot from inside the penalty area around the post for a corner.
The Angolans threatened more at the start of the second half and, after Mendonca's near miss in the 54th minute, Flavio claimed his nation's first ever World Cup goal on the hour when he was left unmarked to head home Jose Ze Kalanga's cross from the right.
Mendonca should have extended the lead three minutes later when he curled his attempt from the edge of the area well wide and, with 15 minutes to go, the Angolans were to regret that miss as Bakhtiarizadeh steered the ball past Joao Ricardo.