The Australian pair raced through the first set but were pegged back by the fourth seeds in the second before they held their nerves in the tiebreak to clinch their first grand slam title.
Draper, who also made his professional golf debut this week, was a late replacement for fellow countryman Todd Reid, who pulled out on the eve of the event.
Ullyett had been bidding for his second grand slam crown in two days, having teamed up with fellow Zimbabwean Wayne Black to win the men's doubles title on Saturday.
