R Laldanmawia struck in the 58th minute to hand Aizawl three points from the match.
With the win, Aizawl rose to 20 points, one point shy of joint leaders East Bengal and Mohun Bagan.
Meanwhile, Mohun Bagan are now left to be the sole team yet to be beaten in the ongoing season.
The highly anticipated match between Aizawl and East Bengal had a dramatic start with the away side making their attacking moves immediately. However, the home side were not to be intimidated by Trevor Morgan's boys.
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As the game picked up pace, the home side got into their grooves, attacking from both sides.
Towards the end of the first half, Aizawl missed what could have easily been the first goal of the match as Laldanmawia's volley flew high over the crossbar.
Brandon's striking delivery from the left was cleared by Bukenya, but Laldanmawia failed to convert the ball which came his way.
Bukenya saved his team a few minutes later as he thwarted Al-Amna's attempt for the back of the net. Bukenya was kept busy by Aizawl towards the end of the first half.
To the ecstasy of the huge supporters, Laldanmawia beautifully lobbed the well-timed cross unleashed by Jayesh Rane from the left.
East Bengal characteristically attempted to have the fortune reversed in their favour but the attackers were repeatedly outnumbered inside the box.
Robin Singh tried to equalise as he received Rahul Bheke's delivery but his header jammed into Albino's gloves.
Towards the end of the match, East Bengal kept the Aizawl boys on their toes but eventually, the home team had the last laugh.
"We can win the league if my boys truly desire and aspire for it," he said.
East Bengal coach Trevor Morgan admitted his side did not deserve a win.
"Aizawl FC deserved to win. The practice I had with my boys did not translate across in their game today.
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