Iraq twice fell behind to last month's confident AFF Championship winners, but Ali Adnan punished Nguyen Phong Hong Duy's tackle on Safaa Hadi by curling a sublime 20-yard set-piece into the top-right corner.
Vietnam took the lead when Ali Faez comically put through his own net in the 24th minute, but teenage striker Mohanad Ali equalised with a cool finish 11 minutes later.
Nguyen Cong Phuong managed to bundle Park Hang-seo's side back in front before half-time, but Ali Adnan added to Humam Tareq's goal to send Iraq level on points with Iran, who beat Yemen 5-0 on Monday.
Vietnam moved ahead when Ali Faez beat Cong Phuong to a pass into the box and his attempt to turn to safety saw him knock the ball into his own net.
Mohanad Ali pounced on an error from Do Duy Manh and jinked past Que Ngoc Hai before firing into the bottom-left corner, but Vietnam regained their lead in the 42nd minute.
Jalal Hassan Hachim parried a low shot from Nguyen Trong Hoang to his right and Ahmed Ibrahim's attempt to clear went in off Cong Phuong.
Iraq got another equaliser on the hour mark when Vietnam failed to clear after keeper Dang Van Lam kept out Mohanad Ali's header and Tareq picked out the roof of the net.
The turnaround was completed late on when Ali Adnan's exquisite free-kick left Vietnam with nothing to show for their efforts.