Defending champion Rublev stunned by Popyrin in Monte Carlo
Popyrin broke in the third game of the first set, but Rublev broke to take a 3-1 lead in the second, only for the Australian hit back immediately.
A further break made it 5-4 to Popyrin and he held serve to reach the third round for the first time. Russian fifth seed Rublev had received a bye into the second round.
"The idea was not to give him the same ball," Popyrin said.
"He is probably the best player from the baseline when you give him rhythm, so I tried to change the pace, height and spin and I think it worked really well for me today."
Popyrin will face fellow Australian Alex de Minaur next, after the 11th seed beat Dutchman Tallon Griekspoor 2-6, 6-2, 6-3.
Russian 15th seed Karen Khachanov also came from a set down before seeing off Argentine Francisco Cerundolo 4-6, 6-4, 6-3 to advance to the third round.