Roger Federer, who is seeking a record sixth Indian Wells title, extended his win streak to 16 straight matches.
Hyeon Chung's unexpected run to be the first South Korean in a Grand Slam semi-final has drawn new fans to the sport in his homeland where tennis lags far behind golf and baseball in the popularity stakes.
Roger Federer will meet Marin Cilic in the final on Sunday.
Cilic will face either defending champion Roger Federer or unseeded South Korean Chung Hyeon, who play on Friday.
Former World No1 Novak Djokovic lost to Chung Hyeong in straight sets in the fourth round.
Hyeon Chung rallied from a set down to see off Rublev 3-4 (5/7), 4-3 (7/2), 4-2, 4-2 in just under two hours.