Jamshidian settled a contest that saw both sides waste a number of gilt-edged chances with a ninth-minute strike that slipped through the hands of Al Shabab keeper Waleed Abdullah.
Hadi Aghily missed a first-half penalty and Emad Mohammed hit the post in the second period for Sepahan, while Ali Ataif wasted two glorious opportunities for Al Shabab.
The result means Sephan leapfrog their Saudi rivals onto eight points, one behind Pakhtakor who have nine. Al Shabab, meanwhile, remain on seven points with all to play for in the last round of matches.
Jamshidian opened the scoring with just nine minutes on the clock as Abdullah beat away Ehsan Haj Safi's effort but the rebound fell to the midfielder, who volleyed home.
Mehdi Rahmati was called into action for the first time in the 34th minute when the Sepahan keeper pulled off a fine save to deny Flavio at close range after a deflected shot had fallen into the Angolan striker's path.
Sepahan were then handed a great opportunity to double their lead when Abdulmalek Al Khaibri was adjudged to have brought down Safi in the box.
Aghily stepped up to stroke the ball into the bottom corner but Waleed did well to turn his effort round the post low down to his right.
Mehdi Karimian then directed a free header wide of the far post from six yards out as Sepahan failed to build on their advantage before the break.
The hosts came even closer to a second goal in the 59th minute when Ibrahima Toure's flick on allowed Emad Mohammed to spring the offside trap and bear down on Abdullah's goal but the Iraqi striker’s finish clipped the prone keeper's leg and that was just enough to divert the ball onto the inside of the post.
Ataif then somehow conspired to miss the best chance of the match for Al Shabab six minutes later. Marcelo Camacho's low free-kick reared up and hit Rahmati square in the face and although Ataif was first to the rebound, he blazed over from six yards.
Abdullah then denied Toure from eight yards after Emad Mohammed's fine cross had played the striker in before the latter squandered another opening as a swift Sepahan break saw the forward cut inside a defender into the box but scuff a weak shot past the near post when he should have squared to an unmarked Toure.
Rahmati shovelled another low Camacho free-kick round the post in the 70th minute before Ataif was again guilty of a glaring miss as substitute Fisal bin Sultan slipped the ball through a Sepahan defender's legs on the left side of the box into the path of the onrushing forward, who side-footed the wrong side of the post from six yards.
Rahmati then turned Tareq El Taib's left-foot volley from the edge of the box over the bar in stoppage-time as Sepahan held on to claim a vital win.