It took me several tries too. The trick is to not start turning in on the driving line. Start a little bit to the left of it, make sure you're in the first gear, slow down to the point when the line is green and just roll through the corner. Be patient, don't accelerate until you are sure you won't have to use the curb when coming out of the hairpin.
Basically stay on the racing line at all times apart from the very start when you need to deviate a bit to the left of it. I found Porsche 911 GTX Falken to be the best handling car in the game, especially for mastering corners. I think you get it at level 15.
Hope that helps.
