Rublev, the world number 37 who reached the US Open quarter-finals this year, needed just over an hour to see off Coric whose frustrations were summed up by his destruction of two racquets courtside.
In Saturday's final, the Russian will face Hyeon Chung of South Korea who beat Russia's Daniil Medvedev 4-1, 4-1, 3-4 (4/7), 1-4, 4-0.
"Today I played my best tennis of the week. I'm really happy," 20-year-old Rublev told atpworldtour.com.
Rublev finished the semi-final with 17 winners to only eight unforced errors.
Coric, meanwhile, hit 12 winners but 14 unforced errors.
"He was just playing too good for me today. He was the better player on the court," admitted the Croat.
Chung won all of his three group matches to make the semi-finals, including a 4-0, 4-1, 4-3 (7/1) victory over Rublev. He also saw off the Russian in Winston-Salem on the ATP Tour in August.
"I had to stay calm," Chung said after seeing off Medvedev.
"I was just trying to stay calm and he was playing good, so I had to play the same as I did in the first and second set."
On Saturday's match, the South Korean said: "I need a rest because it's already midnight, so I have to do my recovery first.
"We know how to play each other, so I have to go sleep, only."