After a goalless first half, Qatar took the lead in the 62nd minute through a Bassam Hisham free-kick.
The goal proved to be enough to see the Gulf nation advance to the next round of the tournament.
Elsewhere on Tuesday, South Korea defeated Bahrain 2-1 to progress to the next round.
Mohamed Marzooq’s strike on 77 minutes canceled out Hee-Chan Hwang’s 43rd-minute opener to force extra-time, but Jin-Su Kim put his team back in front with a goal in the first half of ET.
South Korea joins UAE, Australia, Vietnam, Japan, China, Iran, and Qatar in the quarter-finals of the tournament.
The matches will be played on Jan.
24 and 25.
The 2019 Asian Cup began on Jan.
5 and will continue until Feb.
For the first time, Asia’s largest continental tournament includes 24 teams instead of the traditional 16-team format used in previous competitions.
Iraq finished runners-up to Iran in group D, beating Vietnam 3-2 and Yemen 3-0 before a 0-0 draw with Iran.
Iraq’s most notable triumph at the international level came in 2007 when they were crowned Asian Cup champions, beating Saudi Arabia 1-0 in the final.
Iraq is 80th in FIFA’s world rankings (their highest ever rank was 39 in 2004).
They have failed to qualify for the FIFA World Cup since their maiden appearance at the Mexico 1986 tournament where they lost all three of their group matches.