British number one Norie fought hard to beat Draper 7-6 (7-5) 6-4 to reach the third round of the Miami Open.
"I had a little bit of nerves - I was a big favorite against a young Brit. I'm excited to see how he performs in the future," Nori told Amazon Prime.
Nori will next face France's Hugo Gaston as he tries to reach the fourth round for the first time.
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