Bufff, finally done. I found it interesting but extremely difficult and random, that's the reason I won't give five stars unless I am wrong and there is a reproducible way to win it. Thanks for sharing!
No there isn't. Depending on your skill and resulting speed of the balls, there is a 1-25% chance it will work (rough guess). If it doesn't work "don't feel gutted" and retry. But I would never put something like this not as first step in a level.
The only way I could consistently reproduce my efforts was to have B knock each ball down. Spoiler Chasing the final ball down the "sidewalk" not sending it down the gutter Does that count?