After a barren first half at the Bangabandhu National Stadium, Nixon scored the match-winning goal for Ctg Abahani in the 77th minute (1-0).
Despite the day's win, the port city team remained at the seventh slot in the league table, securing 19 points.
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Muktijoddha slipped to 11th place with nine points from 12 matches, suffering seven defeats.
The first phase matches will conclude on Sunday with Sheikh Jamal and Mohammedan SC match. The game will kick off at 4pm at the Bangabandhu National Stadium.
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Three times champions Sheikh Jamal, now in the third spot in the league table, just need a victory in Sunday's match to advance to the second slot, toppling Dhaka Abahani.
Federation Cup champions Bashundhara Kings, also a former league champions, has comfortably dominated the ongoing league securing 34 points from 12 matches.
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Six times champions Dhaka Abahani and former champions Sheikh Jamal has followed the leader distantly with 25 and 23 points from 12 and 11 matches.