The fifth-seeded Rublev led 6-4, 4-1 when Anderson quit the match with a right thigh issue.
Anderson, who won the event in 2018, wore tape on his thigh from the start of the match. He first got a medical timeout after losing the opening game of the second set and asked for treatment again at 3-0 before playing just two more games.
It was the second time this week that Rublev’s opponent quit their match, after Jannik Sinner pulled out after three games with a foot injury in the second round.
The eighth-ranked Rublev is 4-0 in finals in this shortened season and can become the first player with five tournament wins.
Coming off back-to-back wins in Hamburg and St. Petersburg, Rublev improved to 18-1 in his last four events.
“I came here thinking I had nothing to lose,” Rublev said. “I came here to enjoy, to do my best, to fight for every point every match. Now I am in the final, I will keep thinking the same way.”
In the opening set, Rublev and Anderson eased through their service games until 5-4, when Anderson held off two break points before double-faulting on a third. Rublev, who served 11 aces, has not lost a service game all tournament.
After undergoing knee surgery twice, Anderson was seeking his first final since earning his sixth career title in Pune, India, in January 2019.