Using the Subaru Impreza 2.5 RS, or some other cars,on most drift tracks you can hold the handbreak the whole time around the track. "Wag" the car from left to right on the straights.

Complete "Go Underground" Mode
When you are at the starting line and it's say 3..2...... and so on. Keep reving your car. Don't keep A on or it'll skid and you'll have a bad start. When your off racing, when you get to a corner get really close to the corners but don't hit them! You are getting more in front of the oponent(s). When you get to a straight don't turn one bit. Carry on going and you catch so much speed! You will be flying ahead now. When you turn a corner don't let go of A only if it looks like your going to hit the wall. Then slam it straight on again after. Keep this up all the way through the track. Make sure you don't waste your Nitrous because your gonna need it for the straights. You can now win easily.