Nadal, 32, showcased his new serve during a 6-4 6-3 7-5 victory over the Australian wildcard in warm weather on Rod Laver Arena.
The Spanish 17-time grand slam champion seemed to have some extra speed on his serve, which was broken just twice.
The second seed was largely untroubled by Duckworth, who is ranked 237th in the world, in his first competitive match since the US Open in September.
Duckworth was aggressive early, including serving and volleying, but a double fault handed Nadal a break in the opening game.
The Australian was unable to get back into the set, but he did break early in the second.
However, his advantage was short-lived – giving the break up from 40-0 – before Nadal took complete control.
Nadal was in fine form, breaking again in the sixth game of the third, only to squander it when serving for the match at 5-3.
Nadal responded quickly, breaking in the 12th game and sealing victory with a backhand cross-court pass.
He will face either Matthew Ebden or Jan-Lennard Struff in the second round, with a potential match-up against Australia's highest-ranked male player - Alex de Minaur - in the the third round.