Draper and Boulter have each produced career-best seasons in terms of winning tour titles and climbing the world rankings.
Draper, having become more physically robust this year, also reached the semi-finals of a Grand Slam for the first time at the US Open in September.
A demanding win over Machac – who world number 18 Draper beat in the fourth round of his New York run – was another example of the improvements he has made.
Using his first serve effectively, covering the court to outlast Machac in baseline rallies, and adding variety to plant doubt in his opponent’s mind were the keys to an impressive opening set.
He also needed to show the gritty side of his game.
Fending off six break points for 27th-ranked Machac kept Draper in command and, although he succumbed to a seventh which decisively turned the second set, the British left-hander regrouped to dominate the decider.
“I felt it was more of a mental battle,” said Draper.
“My energy dropped a little bit and my decision-making became up and down.
“At this level you can’t get away with spending too long in that situation. I’m proud how I dug in.”
Despite raising concerns recently about the demands placed on leading players, the seventh seed has looked sharp at the ATP 500 event.
Draper will face German top seed Alexander Zverev or Italian sixth seed Lorenzo Musetti in Saturday’s semi-finals.
“I’m improving all the time and my results are showing that,” added Draper, who is set to rise to another new career-high ranking whatever happens over the weekend.
“I’m working hard to become more consistent. It’s showing.”