The key thing you need to answer that question is when that CC reports to the credit bureaus (also known as consumer reporting agencies or CRAs). Because your score is driven off information reported to the three CRAs, your new balance will have to get reported before your score could change.
Most credit card companies (CCCs) report to the CRAs 1-2 business days after your statement prints, and the amount they report is the "Amount Owed" at the top of the statement.
So when you are trying to get your reported CC balance to change with the CRAs, what you typically want to do is make your extra payment a week before the statement is supposed to print. I say a week before just so enough time goes by for the transaction to clear your bank and the CC. 2-3 business days might be plenty, but better to make the payment a week before if you want to be certain. Then you probably want to give it a week AFTER the statement prints before you can be confident that the amount has been reported and the CRA has updated its records.
Most CCCs report shortly after the statement prints, but not all of them do. Some report around the 1st of the month (say). If you want to know for sure, you can join Credit Karma and pull your reports there. You will be able to see the exact date your CCC reported to Equifax and to TransUnion.
