Mahmood struck from close range on the stroke of half-time to give the Zico-coached Iraqis the lead after China had dominated the opening period but were unable to find the back of the net.
The defeat leaves China struggling in third place in Group A of the third phase of Asias qualifying tournament for the 2014 FIFA World Cup.
Only the top two teams progress to the final phase of qualifying and Jordan lead the group with nine points and three games left to play. Iraq are second on six points, three ahead of China, with Singapore in last place on zero.
"Im happy that we won this game and we played well under abnormal conditions," said Zico. "It was a tough game and it was the second time we faced this problem of playing with 10 men.
"China played well and I have to give many thanks to my goalkeeper because he did a great job."