William Opoku scored the all-important goal for Minerva in the 77th minute.
The win took Minerva to the second place with 11 points from seven matches, behind table-toppers Chennai City FC (17 points from 7 matches).
For East Bengal (6 points from 5 matches), it was their third loss in five games and they now move further down to eighth out of 11 teams.
Both the sides made two changes to their starting line-up from their previous games.
East Bengal's Spanish coach Alejandro Menendez Garcia gave midfielder Kasim Aidara his first start of the season against his former club and also got in Yami Longwah. Both the Raltes, Laldanmawia and Lalrindika, made way for them.
Minerva's Irish coach Paul Munster, on the other hand, played Nigerian defensive midfielder Bala Hassan Dahir in place of countryman Donatus Edafe and in a straight defensive swap, brought in Akashdeep Singh in place of Arashpreet Singh.
The first half was a battle of attrition with no clear cut chances being created. East Bengal had the best of two half-chances, both created by striker Jobby Justin.
Esqueda missed the first while Brandon Vanlalremdika was at the end of the other but both attempts went wide.
The second half began in more entertaining fashion. The home side were more enterprising to begin with but a couple of substitutions on each side, particularly those made by Minerva, changed the complexion of the game, as far as goal scoring chances were concerned.
The first corner of the game went Minerva's way in the 56th minute and they got two on the bounce but to no avail.
Opoku got the best chance of the game in the 57th minute when he was played on by substitute Moinuddin on the right of the box and his strike brought about a good save by Ubaid to thwart the Ghanaian.
Esqueda, in the 62nd minute, took advantage of a poor clearance by Minerva defence, to unleash a crisp half-volley but Arshdeep in the Minerva goal was equal to it.
Opoku then tried to create a chance when he latched on to a ball and cut in from the right to unleash a fine ball for Donatus Edafe rushing in from the left. The Nigerian's effort with only the goalkeeper to beat from six yards out was not only weak but also off target.
Opoku finally got the goal he wanted when Minerva caught East Bengal on the break and Moinuddin floated in a cross from the left flank which pierced an onrushing Ubaid and a retreating Manoj Mohammad to land perfectly at the feet of Ghanaian whose first time connection went into the empty net.
It was his second strike in three games.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)