In a racing type situation, it is referred to as being in the lead. Hence the dust stirred up from behind them is what one would experience in the face or mouth.
It generally means to put a very light coating of some kind of powdered material on top of something. Like: Dust the top of each dish of custard with cinnamon, or dust the doughnuts with powdered...
Although the saying has been used inappropriately (or humorously) to its true origin, the following should shed some light on its beginnings. Tim Moore: The Gold dust Twins As a youth, Tim Moore...