The quickest way I found to do these is to hold the A button and Right Trigger from the start, during the countdown. This will allow you to tag your opponent from behind. Get to the point where you know you can coast up for the tag and let go.
If you fail, the game tells you to Tilt around so you can go the other way. The easier way to do this is to Powerslide in which ever direction you have more room in. This allows you to maintain speed and you can utilize any boost you have for a speedy get away.
Basically, gas and boost to the tag, coast into the tag, powerslide around and boost, and just boost whenever to get to the finish.!