All you have to do is start off with a slow a steady pace and stay behind her, and right near the end start pounding down on the button to pass her and not give her a chance to get back ahead of you. I use the method like Starmud mentioned "hold the 'thumb' right above the button and like strain the underarm (tense your arm so your hand shakes, weird I know, but it works.) It will start shaking, pressing the button rapidly."
But yes, all you have to do is be patient and go the slow a steady route, and then turn it up at the end to beat her. No other way to win, especially for the second race for the cheat note in the Cloud level, trust me, it's a long race...