Draper had got off to the perfect start against Nakashima with an early break but the rest of his day was far from straightforward.
But, as he has increasingly been showing in a year that has taken him to a career-high fourth in the world, he manages to bring out his best tennis in the most difficult moments.
From the second-serve ace that warded off a break to a brave drop shot at 15-40, Draper showed he is not afraid to take risks and this confident approach is paying off here.
Having lost the second set to world number 32 Nakashima when he sent a forehand long, Draper tightened up on his errors in the third and broke serve in the seventh game with one of the stunning forehand winners that have become a hallmark of his game.
He had thought he had sealed the game on the previous point with a backhand but the automatic line call of “out” had been drowned out by the crowd’s cheers.
He had to save a break point while serving for the match at 5-4 but recovered to seal victory after two hours and 22 minutes, delivering a 14th ace during that final game.
“I think at times I’ve not played some great tennis and in those moments I’ve just tried to believe in myself and I think that is where the confidence has come from,” Draper said after reaching a 12th Tour-level semi-final and his fourth of the year.
“Hopefully, I can carry on to the next round and get better.”
He will now play only his second last-four match on home soil after reaching the semi-finals at Eastbourne in 2022.
His progress here will help his preparations for Wimbledon, which starts on 30 June, and the top-four seeding is a bonus for him going into the grass-court Grand Slam where he will be viewed as the great home hope.
“Last year I went there [to Wimbledon] ranked 40th and now I’m fourth. To get to that position is an incredible feeling,” he said. “It is testament to the work me and my team have done and I am proud of that.”
