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 on Tuesday 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.
There is extra attention on the event this year after three of the nations blockading Qatar – Saudi Arabia, the United Arab Emirates and Bahrain – reversed their decision to boycott the event due to a two-year diplomatic dispute.
The trio, along with Egypt, continues to impose a land, air and sea blockade on Qatar after severing ties in June 2017 and accusing it of “supporting terrorism”, a charge repeatedly and vehemently rejected by Doha.
The three neighbouring teams landed in Doha on Monday, with some media reports suggesting that the Saudi team took a direct flight from Riyadh to Doha, despite a ban on direct travel.
Speaking to Al Jazeera on Monday, Ali al-Salat, head of media for the 24th Arabian Gulf Cup, said: “It’s a good thing that we have the eight countries participating in this edition.”
“It gives more media coverage, more excitement, more matches to watch, so I think its something really good for the region.”
“We are here just to play football, to enjoy football … we don’t want to mix sports and politics.”
Khalid al-Mohannadi, a Qatari football fan, who was unable to attend his side’s opening match on Tuesday, said: “This Cup is for the people, not the government or politics.”
Follow Saba Aziz on Twitter: @saba_aziz