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Paying off a closed account should not in itself cause a score drop. What can happen is that paying off a credit card can cause certain credit monitoring tools (e.g. myFICO Ultimate) to send you an alert indicating that you paid the card to zero. At the same time the tool will recalculate your score. If something else changed on your report since your score was generated (very possible and such changes are often difficult to see) that might well cause a score drop.
When your card reported a zero balance, were all your cards at zero? Just curious.
Unstated in the post is whether the account was being reported as delinquent based on the discrepancy in balances.
Was the minimum payment being made each month, or was the payment less than the min, resulting in a delinquency status?
You got hit for having utilization at 0. Let a balance report on one of your cards this month and you will probably see those points return.