Conditions were far from ideal for a free-flowing game as the players found the pitch slippery under foot following a heavy downpour in the second half.
Earlier, Karrar Jassim, the Iraq international, who was sent off for dissent in the 73rd minute, put the visitors ahead with a strike on 12 minutes.
Kabi doubled the lead four minutes before the break and regained the two-goal cushion for Ajman with a powerful header shortly after Luiz Fernando, the Brazilian forward, pulled one back for Dibba.
The Ivorian completed his treble with a goal in the fourth minute of injury time.
The win moved Ajman up a place into 10th on 15 points, while Dibba remain firmly rooted to the bottom of the table on four.
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