In fast-rising Draper, 21, the 22-time Grand Slam champion faced a stern test to start his campaign at a sweltering Melbourne Park.
The top seed recovered from a second-set wobble — and a bizarre incident when a ball boy accidentally took his racquet — to defeat the 38th-ranked Briton 7-5, 2-6, 6-4, 6-1 at Rod Laver Arena.
Nadal, who recently became a father, faces American Mackenzie McDonald in round two.
“Very exciting, new beginning, just super-happy to be back at Rod Laver with a victory I needed,” he said after grinding down Draper.
“Last couple of months have not been easy for me.”
Nadal was on court when Australia’s talented but temperamental Kyrgios called a hastily arranged press conference and announced that he was out of the tournament with a knee injury.
“I’m devastated, obviously,” said the Wimbledon finalist, who was considered an outside bet to win a maiden Grand Slam crown.
“I’ve had some great tournaments here, winning the doubles last year and playing the tennis of my life probably going into this event.
“I’m just exhausted from everything, and (it’s) obviously pretty brutal.”
The first Grand Slam of the year had already lost several stars in the build-up.
Injured men’s world number one Carlos Alcaraz and two-time Melbourne champion Naomi Osaka — who is expecting her first child — are among the other players missing.
Nine-time Australian Open champion Novak Djokovic, who was detained and deported ahead of last year’s tournament after refusing to get vaccinated for Covid, begins his title assault on Tuesday.
Other winners on Monday included third seed Stefanos Tsitsipas and sixth seed Felix Auger-Aliassime, who saw off dogged Vasek Pospisil in an all-Canadian clash.
Russia’s Daniil Medvedev, losing finalist in 2021 and 2022, fired up his bid to go one better with a straight-sets demolition of Marcos Giron.
But 21st seed Borna Coric fell to Czech player Jiri Lehecka in straight sets.
‘Focused on myself’
In the women’s draw, hot favourite Swiatek was far from her fluent best against Jule Niemeier but got the job done, 6-4, 7-5.
“Honestly, I wanted to be focused on myself because I know that Jule serves amazing and was really pushing, putting pressure on me,” said Swiatek, who landed only 49 percent of her first serves.
“So I’m pretty happy that I got through this match because the first round is always tricky and I guess an opponent like Jule makes it even more tricky.”
The Pole, who is chasing an Australian Open crown to go with major titles at the US Open and Roland Garros, plays Camila Osorio of Colombia next.
In-form Pegula blitzed 161st-ranked Romanian Jaqueline Cristian 6-0, 6-1 in a 59-minute romp to signal her intent.
Fellow American Gauff was equally explosive in racing into the second round with a 6-1, 6-4 thumping of Czech Katerina Siniakova.
The 18-year-old Gauff now faces a mouth-watering encounter against former US Open champion Emma Raducanu.
It will be the first-ever meeting between Gauff and the 20-year-old Raducanu, two rising stars of women’s tennis.
“I’m really looking forward to this match,” Raducanu said.
“I’m very up for it. Coco has obviously done a lot of great things and she’s playing well.
“I think we’re both good, young players, we’re both coming through — part of the next generation of tennis really — it’s going to be a great match.”
Also safely through was another American, Danielle Collins, last year’s beaten finalist in Melbourne.
Greek sixth seed Maria Sakkari also won and Victoria Azarenka defeated Sofia Kenin in a battle of two former Australian Open champions.
But two seeds fell at the first hurdle, 25th-seeded Czech Marie Bouzkova and American 28th seed Amanda Anisimova.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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