Following a goalless first-half, the hosts went in front in the 54th minute when Aghily converted from the spot after Ibrahima Toure had been brought down in the box.
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 on the verge of a place in the last 16. Al Gharafa, meanwhile, are yet to find the back of the net in three 2011 AFC Champions League games.
The opening 45 minutes proved light on both entertainment and chances with Fabio Januario's fierce strike from 25 yards that flew just off target with Burhan – wearing a protective mask - scrambling across his goal the closest either side came to breaking the deadlock.
But the game sprang to life in the second period when Sepahan took the lead nine minutes after the break.
Toure brought down a high ball in the box but before the striker could advance on goal he was felled by Al Gharafa defender Bilal Mohamed.
Aghiliy stepped up and coolly side-footed home the resultant penalty, sending Burhan the wrong way.
Toure had a great chance to double Sepahan's lead in the 63rd minute but he side-footed a low cross wide from eight yards when unmarked.
The miss did not prove costly, though, as two minutes later Jamshidian netted the second goal when he beat Burhan at his near post from 25 yards with the keeper rooted to his line.
The Al Gharafa keeper had to be at full stretch to turn another Jamshidian effort from distance around the post in the 67th minute.
Amare Diane flashed a dangerous cross across the Sepahan six-yard box but nobody could apply the finish before Januario tried to lob Burhan but the ball landed on top of the net.
Juninho's dipping free-kick with nine minutes to go saw Sepahan keeper Mahdi Rahmati forced into a scrambling save with his knees and Otman El Assas curled a shot just past the post as Al Gharafa threatened a late comeback.
Toure then shot tamely at Burhan at the other end and substitute Hossein Papi could not hit the target from 40 yards after the Al Gharafa keeper had come charging out of his goal in stoppage time.