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.
"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."
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.
"It was a shock to concede a goal so late in the game," he said. "It is hard but the players must be strong."
