The result comes 11 days after Raducanu left the court in tears after retiring from her round of 16 match at the ASB Classic with an ankle injury. She wore strapping around her left ankle during her win over Korpatsch.
“Everything I’ve done has been quite controlled the last week,” she said.
“So I had to test it out in a real match, with the unpredictability and just getting used to it in the beginning. It felt good. You know it’s there and if anything, it kind of alleviates any pressure.
“That’s because you’re, like, I’ve done so well to get myself onto the court, and my team has done so well. It’s a great achievement for all of us.”
Raducanu, 20, will face 18-year-old World No. 7 Coco Gauff in the second round.
After being edged 7-5 in the first set, Draper rallied to win the following set 6-2. However, the 21-year-old, who was suffering with cramp, could not prevent an onslaught which saw the Spaniard round off the game with a 6-4, 6-1 recovery.
“I played one of the toughest possible opponents in the first round,” Nadal said.
“He is young, he has power and has a great future ahead. We will see him play for many years ahead.”
Cameron Norrie defeated Luca van Assche in straight sets to be the first Brit to enter the second round in the men’s draw.
Norrie, British No. 1, edged the first set 7-6 (3) before cruising the next two 6-0, 6-3 to set up a tie against Constant Lestienne.