The 24-year-old Muscovite came in fourth place.
He was ahead of compatriot Daniil Medvedev, who dropped to fifth place.
Russian Karen Khachanov takes 30th place, Aslan Karatsev - 50th.
Spaniard Rafael Nadal is the leader of the championship race.
His compatriot Carlos Alcaraz, who won the Masters series tournament in Madrid, climbed to second place.
Stefanos Tsitsipas from Greece dropped to third place.
Earlier it was reported that Rublev rose to seventh place in the ATP rankings.