Matosevic, ranked 55 in the world, will be playing his fifth quarter-final of the season when he faces Argentine star del Potro, who fought for just over three hours to win his opening match on Wednesday.
Slovenia’s Grega Zemlja shattered Australian hopes of seeing two players in the quarter-finals when he defeated Matthew Ebden 7-5, 6-4.
Tomas Berdych reached the quarter-finals at the Stockholm Open with a 6-1, 6-4 win over Estonia’s Jurgen Zopp on Thursday.
The Czech will next face Russia’s Mikhail Youzhny and remains in line to qualify for the season-ending ATP World Tour Finals in London.
Top seeded Jo-Wilfried Tsonga, also hoping to qualify for London, advanced with a 6-3, 7-6 (6) win over Go Soeda of Japan. The Frenchman faces Sergiy Stakhovsky of Ukraine in the quarter-finals after Stakhovsky beat Spain’s Feliciano Lopez, 7-6 (5), 7-5.
Marcos Baghdatis of Cyprus advanced when Alejandro Falla of Colombia retired because of a left foot injury while trailing 6-0, 3-0. Baghdatis next faces Lithuania’s Ricardas Berankis.
Top-seeded Roberta Vinci of Italy reached the Luxembourg Open quarter-finals by beating Anne Keothavong of Britain 6-4, 6-1.
Venus Williams, playing her first tournament since the US Open, also advanced with a tough 7-6 (7/4), 6-4 victory over German Mona Barthel.
Andrea Petkovic of Germany defeated third-seed Jelena Jankovic of Serbia 7-5, 6-0, while Daniela Hantuchova of Slovakia defeated Kirsten Flipkens 6-4, 4-6, 6-2.
In another second-round match, Ksenia Pervak of Kazakhstan beat sixth-seeded Sorana Cirstea of Romania 7-6 (4), 6-1.