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Following the match at Bangabandhu National Stadium, Chittagong Abahani remained at the seventh slot in the points table, collecting nine points from eight matches.
And Police secured the eighth spot bagging the same number of points from seven outings.
Chittagong Abahani dominated the first half 2-0. Brazilian forward Nixon Brizolara put Abahani ahead in the 18th minute, scoring the match's first and his sixth goal in the league (1-0).
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Local midfielder Rakib Hossain doubled the lead scoring the second goal for the port city team (2-0).
Rakib widened Abahani's margin scoring his second and the third goal for his team in the 49th minute (3-0).
After trailing by 0-3, three Ivory Coast booters came to Police's rescue and snatched one important point from Abahani, scoring three goals in a row within 32 minutes.
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Midfielder Frederic Pooda scored for Police in the 58th minute (3-1), defender Lancine Toure netted the second goal in the 75th minute (3-2), and Bollo Famoussa levelled the margin in the stoppage time of the match from a penalty (3-3).
In the day's other match, Dhaka Mohammedan beat Brothers Union Club 2-1 at the floodlight Bangabandhu National Stadium in the evening.
Swedish-born Bangladeshi booter Joseph Nur Rahman scored first for Gopibagh outfit Brothers in the 11th minute (1-0) while Amir Hakim Bappy equalised for Mohammedan in the 70th minute (1-1).
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Souleymane Diabate of Mali scored the match-winner for The Black and Whites in the 73rd minute (2-1).
Brothers' Faisal Mahmud received a red card in the stoppage time of the match.
With the day's feat, Dhaka Mohammedan occupied the sixth slot in the league table, collecting 12 points from eight encounters while Brothers Union remained at the 12th place in the 13-team league with only one point.