Terrell Owens Scores in Court

Sources close to T.O. tell TMZ, the former NFL star was able to convince the judges in each of his child support cases to "drastically decrease the amount he was paying."

T.O. had originally been ordered to pay between $5,000 and $20,000 per child per month -- and with no new football contract, he was seriously struggling to make ends meet.

But now, we're told the new payment plans -- the details of which are sealed -- are way more affordable ... and "accurately reflect the amount of money [Terrell] is making."

It gets even better -- we're told T.O. was also able to establish visitation in some cases, something he had never asked for before.