Both Draper and Poulter produced career-best seasons in terms of winning tour titles and climbing the world rankings.
Draper, who has become more physical this year, also reached the semifinals of a Grand Slam for the first time at the US Open in September.
The narrow win over Macak – who was beaten by world number 18 Draper in the fourth round of his career in New York – was another example of the improvements he has made.
Using his first serve effectively, covering the court to outmaneuver Mattak on his backhand, and adding variety to sow doubt in his opponent’s mind, was the key to a great opening set.
He also needed to show the brave side of his game.
The 27th-seeded Mattack saved six break points to maintain control over Draper, and although he lost the seventh set that decided the second set, the British left-hander regrouped to take control of the decider.
“I felt like it was more of a mental battle,” Draper said.
“My energy has gone down a bit and my decision making has been up and down.
“At this level, you can’t get away with being in that position for too long. I’m proud of the way I held on.”
Despite recent growing concerns about the demands placed on top players, the seventh seed looked sharp in the ATP 500 event.
Draper will face sixth-seeded Italian Lorenzo Musetti, who knocked out top-seeded German Alexander Zverev, in the semi-finals on Saturday.
“I’m improving all the time and my results show that,” added Draper, who is set to move up to another new career ranking whatever happens over the weekend.
“I’m working hard to become more consistent. It shows.”
