Midfielder Mohammed Qasim Majid scored twice for the visiting side in the first half - at the 18th and 27th minute - during the Group A match attended by almost 38,000 spectators at the 40,000-capacity Khalifa International Stadium on Tuesday.
Abdelaziz Hatem opened the scoring for the hosts early in the second half, finding the net at the 49th minute.
Qatar came close to levelling - with an Iraqi header that deflected off the goalpost, as well as a chance during extra time - but were unable to break through the opponent’s defences.
Both Qatar and Iraq have won the Gulf Cup three times, and this is the fourth time Doha is hosting the biennial regional football tournament.
In the second Group A match played at the Abdullah Bin Khalifa Stadium, 2017 finalists UAE recorded a convincing 3-0 win against Yemen.
Defending champions Oman are in Group B where they will be joined by Saudi Arabia, 10-time winners Kuwait and Bahrain in the group stages.
Ali Mabkhout turned in a striking masterclass to ensure the UAE beat Yemen 3-0 and romp straight to the Group A summit.
The UAE’s leading goalscorer in international football struck twice in the first half and added a third after the break to take his overall tally to 58. But he would have hardly been thinking about how high the bar rises with each strike as the UAE went level with Iraq on three points, but took pole in Group A on the basis of a superior goal difference.
Bert van Marwijk’s UAE side outclassed their rivals in all departments, and Yemen may not have had much to show for their efforts, but not for a moment did they seem like a team that had gone winless in seven previous appearances in the competition.
While the UAE’s business was focused on attacking early on, Yemen plied its trade in defence. Both sides worked tenaciously trying to figure the other out and Mabkhout should have done better then drive wide after being found in the Yemen box by a ball from the deep.
The UAE continued to build and a half-hearted Yemeni attempt called Emirates goalkeeper Mohammed Al Shamsi into action for the first time in the 19th as he raced forward to collect a cross from the right.
Three minutes later, the UAE broke the deadlock with Mabkhout popping up jack in the box style to deftly nod home Bandar Al Ahbabi’s looping cross from the right.
Yemen started to flex their muscle at the half hour mark and the mounting pressure won them a freekick in the 34th minute in prime real estate just outside the box in the centre.
However, Abdulwasea Al Matari shot straight into the wall and sent the rebound straight into the hands of Al Shamsi.