It put him into the second round for a 17th time and stretched his win-loss record at Melbourne Park to 77-15.
He will next play Mackenzie McDonald, who beat fellow American Brandon Nakashima in a five-set thriller.
“Super-happy to be back here in Australia one more time. It’s like the 19th season in the professional tour so very excited about this new beginning,” Nadal said after the 3hrs 41mins test in blistering heat on Rod Laver Arena.
“I needed a victory, so that’s the main thing. Doesn’t matter the way. The most important thing today is a victory against a tough opponent.
“We knew it was not going to be perfect… it was not perfect.
“(But) I think I did things well. So satisfied with the victory because that gives me the chance to play again.”
It was a bit of a slog for the 36-year-old Nadal, who had lost six of his past seven matches, including his opening two this year.
Little separated them in a first set notable for a bizarre incident in which Nadal complained one of his racquets had gone missing.
He kept his cool and waited for his chance, which came at 6-5 on Draper’s serve when he earned a set point and converted with a searing cross-court winner.
But Nadal lost focus in the second set as 21-year-old Draper, ranked 38, raised his game and raced to a 4-0 lead before sealing the set.
The Spaniard regrouped and broke early in the third set to move 4-1 in front, winning the long rallies. Draper needed repeated treatment on his upper right leg, but against the odds broke back before Nadal again stepped up.
Draper was clearly struggling, grimacing in pain at times, and Nadal showed no mercy to race through the fourth set to victory.
“I think it’s only cramping what happened at the end to him. Hopefully is nothing important,” said the Spaniard.
“But I think he is in the right position to have a very productive season. I am happy that I was able to win against a great player this afternoon.”
Nadal created history on the same court last year with his five-set victory over Daniil Medvedev in the final.
It saw him claim ownership of the record for most Grand Slam men’s singles titles on 21, ahead of Novak Djokovic and Roger Federer.
He added a 22nd at Roland Garros, while Djokovic won Wimbledon to move onto 21.
Nadal’s 2022 run in Melbourne came in the absence of nine-time champion Djokovic, who is back this year and begins his campaign on Tuesday.