Draper holds off Khachanov for first ATP 500 title in Vienna
It marked a second title for the 22-year-old Briton but his first at an ATP 500 event, his previous success coming in the ATP 250 event in Stuttgart in June.
"To win my first ATP 500, it feels incredible," said Draper, who will break into the top 15 for the first time in his career.
"I am incredibly happy and so proud of myself and my team. I am going to enjoy it."
After easing through the first set and into a 4-0 lead in the second, Draper suddenly found himself on the back foot as the 28-year-old Russian, who won the Almaty tournament last week, reeled off five games on the bounce.
Draper collected himself in time to close out the set and become the first player to win the tournament on his debut since fellow Briton Andy Murray in 2014.
"I was playing so good, and then the momentum shifted," said Draper.
"Honestly, I didn't feel too nervous or tight. I just missed a few balls and made some wrong decisions, and Karen picked up his level.
"That’s a testament to how good he is. He’s a fighter and he’s in great form.
"It got really tight there, but I stayed solid and in a good mental frame. Luckily I was able to come through. It was a relief."
Draper dispatched world number 17 Lorenzo Musetti in the semi-finals 6-2, 6-4 on Saturday and lost just one set during the tournament.