The team emerged victorious with a 1-0 win in the first leg match held in Kolkata on March 5th.
East Bengal had qualified for the third tier of men's AFC club competition by virtue of winning the 2024 Super Cup.
They had topped Group A with seven points to make it to the quarterfinals.
The Red and Gold brigade got off to a dream start as Arkadag goalkeeper Rausl Charyyev could only parry Dimitiros Diamantakos' strike into the path of Bouli, who gleefully tucked home the rebound.
Chances continued to fall the way of the Oscar Bruzon-coached Indian side and they nearly doubled their advantage in the 17th minute when Diamantakos produced a surging run through the middle.
But his low shot crashed against the post with Richard Celis unable to convert the rebound.
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Arkadag looked to regain the advantage but Shanazar Tirkishov dragged his shot wide from just inside the box before an injury to defender Ybrayym Mammedov in the 30th minute saw him replaced by Berdimyrat Rejebov.
The Turkmenistan champions were given a lifeline three minutes later when East Bengal went down to 10 men after Lalchungnunga was shown a second yellow card for a foul on Yazgylych Gurbanov.
Despite playing with a man less, East Bengal were still creating chances with their fast breaks, going close in the 52nd minute when Celis failed to get his header on target off Diamantakos' cross.
Arkadag increased their intensity as the second half wore on with Shamammet Hydyrow forcing a finger tip save from Prabhsukhan Gill from a free-kick in the 76th as they chased an equaliser.
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The home side's persistence finally paid off when Annadurdyyev converted from the spot after Tirkishov was brought down by Sauvik Chakrabarti.
Annadurdyyev made sure of the win when he made a lung bursting run in the added time to sweep home from 13 yards out to take Arkadag through to the semifinals.