East Bengal, who held more of the ball possession, scored through Thongkhosiem Haokip (31st minute) and Lalrindika Ralte (45+1).
The win will take East Bengal to seven points, two points behind leader Mohun Bagan (9pts), while Churchill Brothers, who lost all their three matches, are yet to open their account.
Churchill Brothers midfield once again lacked the creativity to trouble the rival defence. Assistant coach Alfred Fernandes expected a lot from striker Anthony Wolfe but he could not do much except for a couple of shots which lacked direction.
East Bengal who slowly settled down and as the match wore on looked more threatening as they attacked more from the right with Poojary sending dangerous crosses which rival defender Adil Khan dealt well.
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East Bengal had the first real chance in the 16th minute when Mehtab Hussain who moved on the top laid a pass to Trinidad and Tobago striker inside the box but he miscued his shot which went abegging.
Lalrindika Ralte, who troubled the rival defence, then increased the lead in the stoppage time of the first half when his curling shot from a corner found the net.
Churchill Brothers, who lost both their matches, made three changes from their last match against Mumbai FC but could not trouble the rival defence except for a 30-yard shot from Brandon Fernandes which rival keeper T P Rehenesh tipped over.
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