The victory was a ray of light for the beleaguered Iraqi people as they advanced to Wednesday's semi-final in Kuala Lumpur where they could face fierce rivals Iran or South Korea.
Iraq have been thwarted each time at the quarter-final stage at the last three Asian Cups but they were rarely in trouble against the eager but much smaller Vietnamese.
The Iraqis stumbled at the last three continental tournaments to United Arab Emirates (1996), Japan (2000) and China (2004), but they were always in charge against Vietnam, playing in their first Asian Cup for 47 years.
Iraq will learn their semi-final opponent on Sunday when Iran take on South Korea in Malaysia.
"Now the pressure is coming at us, when you win people want one more win, they're never satisfied and now they are thinking of being the champion," Iraq coach Jorvan Vieira said.
"We have a right to dream, but we have to keep our feet on the ground."
The brace took striker Mahmoud's goal tally to three for the tournament, one behind Japan's leading sharpshooter Naohiro Takahara.
Iraq carried on their group-winning exploits where they conquered Australia 3-1 and drew with Thailand and Oman to qualify for only their second-ever Asian Cup semi-final in over 40 years.
Vietnam's Austrian coach Alfred Riedl before the game called on his youthful team to play like men and not boys, but they were physically out-matched by the bigger Iraqi players.
Riedl said Vietnam's lack of size cost them the chance to compete with Iraq and other leading teams in Asia.
"They deserved to win. We had more or less no chances over the 90 minutes to win the match because Iraq had the physical advantage," Riedl said.
"Our players did not have enough power to penetrate, to defend and to be dangerous. The problem is we are too small, we can get a little success in Asia, but generally we cannot have big success in Asia because we are too small."
Iraq scored from their first attack with Mahmoud doing the damage with a glancing header off a Nashat Akram free kick in only the second minute.
The Iraqis used their aerial supremacy to telling effect in the early exchanges with the Vietnamese defending deep and under pressure.
Impressive midfielder Nashat looked close to scoring twice in the opening half, storming through a couple of tackles to fire wide in the fifth minute and hitting the side-netting in another attack on goal nearing half-time.
The Vietnamese gave their excitable supporters some hope when Nguyen Vu Phong's shot was cleared by substitute Ahmed Abid Ali just before the break.
Abid Ali came on for midfielder Haitham Khadir, who came off second best in a 28th-minute challenge with Phung Cong Minh, who was yellow-carded by the referee.
Midfielder Nguyen Vu Phong forced goalkeeper Noor Sabri Abbas to punch clear a dangerous curling free kick shortly after half-time.
But Mahmoud killed off the game with a beautifully-struck free kick in the 66th minute after Karrar Jassim was brought down on the edge of the box.
He curled the ball over the defensive wall and away from the diving goalkeeper Duong Hong Son to put the Iraqis two-up and cruising to the semi-finals.
Güncelleme Tarihi: 21 Temmuz 2007, 20:36