Irwandi is a former spokesman for the Free Aceh Movement (GAM) and negotiator in peace talks with Jakarta.
Two surveys have indicated that Irwandi nabbed the most number of votes in a field of eight candidates, with Azwar probably in third or fourth place.
Azwar was interim governor several months before and after the massive 2004 tsunami that left about 170,000 dead or missing and 500,000 homeless in the province of four million.
He was endorsed by two Muslim parties and appeared poised to take back his office.
Some two million people voted in Monday’s election, which will decide the governorship and other top posts around the province.
The elections come after a peace deal went into effect on August 15, 2005 to end almost three decades of fighting between the Indonesian army and GAM that killed 15,000.
The tsunami - burdening the conflict-ravaged land with more carnage - triggered the peace deal.
As the races wrap up, attention will turn to economic development in one of Indonesia’s most impoverished provinces.
Sidney Jones, an analyst with the International Crisis Group, said: "It’s going to be a test to see whether GAM leaders can deliver more benefits and better benefits than previous officials."
One GAM sympathiser, who almost lost his life after being beaten by soldiers in the conflict and had lost his house to the tsunami, said he supported Irwandi’s rise.
"But he also must also provide us with houses and jobs," he said.
Irwandi has said that he will wait until the official results - expected to be announced in early January - to declare victory.