Stump knows what's up. Still one of my favorite PC games.
You could take a shortcut and then press 0 to reset your car, you would end up near finish line, something like that. I won it fair the first time, but everytime I replayed it I just used the shortcut, because this race was really damn hard.
They patched the race in Mafia 1 to have a difficulty selector at the start, which (optionally) makes it way easier.