The British number one broke the American in the third and seventh games and served out to love to take the first set in 32 minutes.
Paul’s serve was being put under the greater pressure and, while he saved two break points in the third game of the second set, Draper broke him to love in the fifth game to go 3-2 up.
A stunning forehand down the line put Draper 5-2 and a double break ahead and he comfortably won the next game on his serve to win the match in one hour and seven minutes.
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“I felt really good out there,” Draper told Sky Sports. “I know Tommy is a great player and I had to be on him from the off. I felt good.
“I think probably for the players who are from the UK or who don’t play on this surface often, they go into it with the mindset they are not going to be that great on it and, therefore, that can prevent them going further.
“I know I can play well on this surface and this year it’s been a big goal of mine to prove that I can play really well. I know that if I want to be a top player that I have to.”
The powerful forehand of Draper, who did not face a break point in the match, was in good working order throughout as he hit 13 of his 20 winners with it.
