The world number 10, who has recently been praised by both Roger Federer and Rafael Nadal, took the first set 6-2 with ease before Kopriva, making his ATP Tour debut this week, emphatically fought back 6-3 6-2 to secure a memorable comeback victory.
Number three seed Casper Ruud battled past Dennis Novak 6-4 7-6 (7-5), while Benoit Paire, who only had two ATP wins in 2021 before the Hamburg European Open last week, was 6-4 to the good before Tallon Griekspoor was forced to retire due to injury.
Ruud, who has already won two ATP events in 2021 and three in his career, will now meet sixth seed Paire in the quarter-final stage.
But eighth seed Feliciano Lopez did not enjoy similar success as the world number 96 Mikael Ymer fought past the Spaniard to win 6-7 (6-8) 7-6 (9-7) 6-4 and set-up a quarter-final clash with Kopriva.
At the Umag Open in Croatia, third seed Filip Krajinovic breezed past Radu Albot to record a 6-4 6-2 win.
Krajinovic's countryman and number two ranked player Dusan Lajovic also went through with a 7-5 6-4 win against Bernabe Zapata Miralles.