Chung, who won against Canada's Denis Shapovalov on Tuesday, took 68 minutes to beat Rublev 4-0, 4-1, 4-3 (1).
The Next Gen event -- which features eight players under the age of 21 -- is trialing a number of new rules including first-to-four sets and shot clocks.
Shapovalov got his first win of the tournament on Wednesday when he beat wildcard Gianluigi Quinzi 4-1, 4-1, 3-4 (5), 4-3 (5).
In Wednesday's late match, Borna Coric joined Chung in the semifinals with his second win in as many days.
The Croatian beat Daniil Medvedev 4-3 (5), 2-4, 4-1, 4-2 in an hour and 34 minutes.