World No 1 and tournament organiser Djokovic followed up his wins over Borna Coric and Pefja Krstin on Saturday with a 4-1 4-3(3) victory over Nino Serdarusic.
Rublev also remained unbeaten after an impressive 4-2 4-1 win over Alexander Zverev saw him reach the final, which takes place at 7pm BST, live on Eurosport 2.
Novak Djokovic defends 'phenomenal' Adria Tour
Nick Kyrgios hits back at Borna Coric on Adria Tour - 'Do you have rocks in your head?'
Rublev saved three break points at 2-2 in the first set and then broke serve in the next game to move ahead.
World No 7 Zverev did break in the first game of the second set but lost the next four games in a row to suffer his second defeat of the weekend.
Djokovic was relatively comfortable in his victory over Serdarusic, who entered the tournament on Saturday after Grigor Dimitrov’s withdrawal.
Novak Djokovic hails 'fantastic news' of US Open going ahead
Serdarusic had chances in the opening set but spurned six break points. He was then outclassed in the second-set tiebreak as Djokovic secured the win.
Meanwhile, Coric bounced back from defeat to Djokovic on Saturday with a 4-3 (4), 4-3 (2) win over Krstin and Danilo Petrovic beat Marin Cilic 4-2 4-2.
Dominic Thiem defends Novak Djokovic: 'He didn't break any law'
Novak Djokovic: Criticism after Adria Tour a witch-hunt