Each team struck the woodwork twice in an entertaining, attacking match before Iraq captain Younus Mahmood's cross was deflected by Abbas past Majed Naser who was helpless in goal.
Iraq are second in Group D with three points from two matches, three behind Iran who earlier beat North Korea 1-0 to qualify for the quarter-finals.
UAE face Iran, who are guaranteed first place in the pool, in their final group match on Wednesday while Iraq play the Koreans.
"When you score... and the defender from the UAE gives the last touch it is a little bit lucky but the good thing is we tried to force our luck all the time, in the first half especially we played very well," Iraq's German coach Wolfgang Sidka told reporters.
"It is good we have everything in our hands. Nothing is won. The three points are very good for our confidence."
CAGEY OPENING
After a cagey opening 20 minutes the game burst in to life when Hamdan Al Kamali glanced a header against the post with Iraq keeper Mohammed Kassid motionless.
Iraq, who lost their opening match 2-1 to arch-rivals Iran, responded well and were unlucky not to take the lead when midfield duo Nashat Akram and Qusay Muneer were denied by the woodwork in quick succession.
Akram hit the crossbar with a header from a corner in the 38th minute before UAE frantically cleared the rebound, and then Muneer's 22-metre drive struck the outside of the post.
Both sides continued to go forward in the second half and UAE striker Ismail Al Hammadi was unfortunate to see his fearsome drive crash against the crossbar just after the hour.
Abbas then collapsed to the ground with his head in his hands after his late own goal.
Coach Srecko Katanec was in despondent mood after UAE failed to score for the third consecutive match.
"It was a shock to concede a goal so late in the game," he said. "It is hard but the players must be strong."
