Drakeford was down early but went ahead for the first time when he produced the only birdie of the day between the pair at the 10th and eventually won at the 16th.
Drakeford will now play Frenchman Leonard Bem in the round of 32 on Friday morning.
Earlier in the day New South Wales golfer, Cameron Davis, was eliminated in the preliminary match play round where those who were amongst the ties for the 52nd position and forced to play an elimination round to be inside the top 64 competed.
Davis lost his round to Frenchman Kenny Subregis after leading for much of the match. Subgrgis won the 16th and 17th to eventually win 1 up.