The 22-year-old, playing in his second competition since reaching the US Open semi-finals, won 6-4 7-5 against the Russian world No.24, who had been looking for his second title in seven days.
Draper looked set to breeze to victory on Sunday after going 4-0 up in the second set but was then forced to dig in when Khachanov threatened a comeback by winning the next five games in a row.
The seventh seed became the fourth British player to triumph at the tournament, following in the footsteps of Greg Rusedski, Tim Henman and two-time winner Andy Murray.
"I was playing so good and then the momentum shifted a little bit," Draper said.
"Honestly, I didn't feel like I was too nervous or too tight; I just missed a few balls here and there, maybe a couple of wrong decisions, and Karen started swinging, he started picking up his level.
"That's a testament to how good he is, he's a fighter, obviously on great form.
"It got really tight there for a minute but I stayed solid, I stayed mentally in a good frame and luckily I was able come through when it mattered. But, yeah, it's a relief."
Having already guaranteed a top-15 ranking with his performances this week, Stuttgart Open champion Draper described the match as his "biggest final yet".
Khachanov, who beat Australian second seed Alex de Minaur and 2021 Wimbledon runner-up Matteo Berrettini en route to a second final in seven days following his Almaty Open win in Kazakhstan, was broken from 40-15 up in the third game.
That proved to be the decisive moment in an opening set which was wrapped up in 40 minutes after Draper served strongly and produced an array of eye-catching winners.
Khachanov was twice broken to love at the start of the second set to fall 4-0 behind, but the 28-year-old responded dramatically to move 5-4 ahead before Draper regained his composure to secure his first ATP 500 title after a gruelling hour-and-35-minute contest.
"There are so many amazing players in this draw and to win my first ATP 500 it feels incredible," added Draper.
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