Fellow lefthander Draper played superbly to level the match at a set all on a warm and humid afternoon at Rod Laver Arena but the Briton was soon overwhelmed by cramping and bowed out groaning in pain.
It was something of an escape for top seed Nadal, who came into the match with only one win since the U.S. Open and was far from his best in a match that threw up unexpected challenges.
"I need a victory, so that's the main thing. Doesn't matter the way," Nadal told reporters.
"I was humble enough to accept that (there were) going to be a little bit ups and downs during the match. Typical thing when you are not in a winning mood.
"If we put it in the perspective of what I've been through in the last six months, it was a positive start.
"I played against one of the toughest opponents possible in the first round. He's young, he has the power and I think he has a great future in front (of him)."
It was a far cry from Nadal's last match at centre court when he came back from two sets down to topple Daniil Medvedev in a classic final and claim his second Australian Open crown.
Yet there was still some drama as, at 4-3 in the opening set, Nadal complained during the change of ends that a ballkid had made off with his racket.
"I need the racket back," he told the chair umpire.
Using a spare, he failed to convert a break point in the next game before the missing racket was returned.
Starting his bid for a record-extending 23rd Grand Slam title, Nadal had to shrug off 46 unforced errors to grind down world number 38 Draper and set up his next match against American Mackenzie McDonald.
Despite Draper's troubles, the Briton broke Nadal in the first game of the fourth set when he swooped on an ambitious drop-shot to slot a winner into an open court.
But Nadal went on to win the next six games in succession to claim the match as Draper's cramping severely curtailed his movement.
"Playing Grand Slam tennis, you've got to be out there, especially playing someone like Rafa, for hours and hours and hours," said Draper, ruefully.
"I feel like if you're not cramping, then that's fine. The pains of playing high-level tennis on the body is tough.
"But when you start cramping, it becomes almost impossible, in all honesty."
