Rublev regained a title he previously won in 2020.
"It feels amazing," said the Russian on court at the end. "It’s my first ever title that I won twice."
Both men had battled to the final with demanding victories in the quarter-finals and semi-finals.
"I think both of us were really tired after two three-set matches that finished late," said Rublev. "We were exhausted and it was difficult, but somehow we were able to play at a good level."
After the first 11 games went with serve, Rublev broke the Briton to take the first set.
The second set followed a similar pattern with Draper gaining the only break in the 11th game before holding serve to level the match.
"When I lost the second set, I let it go and started to play more freely," said Rublev.
He took control in the third set, breaking in the second and fourth games to lead 5-0. After Draper finally held, Rublev served out a love game to win the match in two hours and one minute.
"I played at a good level," said Rublev. "In some moments, I was really good mentally and didn't let frustration get over me. As soon as I was frustrated, I was able to restart again and I was able to play at the same intensity. That's the most important thing."
It was his 17th ATP Tour title, but his first since winning in Madrid last May.
