The Serbian superstar cruised into the semifinal with a straight-set victory, while second seed Daniil Medvedev got knocked out.
Spaniard Carreno Busta eased past Filip Krajinovic in straight sets to win the Hamburg European Open title.
The second seed survived a tie-breaker in the first set before running away with the match in the second to set up a final date with Filip Krajinovic.
The top seed Russian lost the first set, but came back impressively in the semifinals to defeat Pablo Carreno Busta.
The Russian wins his match in straight sets to set up a mouth-watering last-eight date with Stefanos Tsitsipas.
Stefanos Tsitsipas defeated American John Isner 5-7.6-3, 7-6(4), 6-1 to go through to the fourth round of French Open 2021.
Rafael Nadal beat compatriot Pablo Carreno Busta in the second semi-final of the Barcelona Open on Saturday to book a summit clash against Stefanos Tsitsipas.
Carreno Busta survives a three-set battle to win in Marbella; Sonego bags the singles and doubles titles in Cagliari
The World No 15 Pablo Carreno Busta overcomes compatriot Albert Ramos Vinolas in a three-set thriller to enter the final