Has a FIBA World Cup game ever ended 61-59?
Exactly once. On January 25, 1959, Argentina beat Egypt 61-59, and no FIBA World Cup game before or since has ended that way. When it happened it was a scorigami, the first 61-59 in league history.
That makes 61-59 the 475th most common final score out of 1,178 that have ever occurred in FIBA World Cup. One point away, 62-59 has happened 1 times and 61-60 has happened 2 times.