Following a goalless first-half, the hosts went in front in the 54th minute when Hadi Aghily converted from the spot after Ibrahima Toure had been brought down in the box.
Ahmad Jamshidian then wrapped up the points 11 minutes later when he beat Al Gharafa keeper Qasem Burhan from long range with a swerving strike to leave the Iranians top of Group A on nine points, three ahead of Al Hilal and eight ahead of both Al Gharafa and Al Jazira.
“We still can't say that we are qualified 100% to the next stage because our main opponent is Al Hilal so if we can beat them, we are certainly going to be in the next round.
"We were there better side in the second-half and we could play a better game to compensate our somehow bad performance in the first-half.
“It is true that we won the match but the more important point was that we could perform our tactical plans well in the game.
"However, despite playing a good game we still have some problems and we have to solve them in the next stages.
"We increased the pace of the match in the second period and through that, Al Gharafa lost their concentration and we scored the second goal.
“Esfahan should be honoured that they have such a great and professional team like Sepahan and I would like to stay here if the managers and the president of the club want me to.”
Opposite number Bruno Metsu saw Al Gharafa fail to score for the third consecutive game but the Frenchman refused to give up hope of reaching the knockout stage.
“We had good goal scoring opportunities in the first-half but were unable to score. I am completely satisfied with my team in the first-half but I cannot say that we played well in the second-half because Sepahan is a very strong team and they could put a lot of pressure on us," he said.
“We are still in the tournament and we still have a chance to qualify to the next stage. What we need to do is to win all our remaining games and try to solve our problems and weaknesses.
“Sepahan are a very good team who can take advantage from any opportunity and they can even be the champions even though it is impossible to predict it for sure at the moment.”
"I had expected to end Al Gharafa's failure in Iran but unfortunately we lost our confidence in the second-half which caused us not to perform our tactical plans in the game."