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|Stefanos Tsitsipas has lost more matches than he has won in 2020. AFP/Koen SUYK|
The world number six, who was knocked out of the Australian Open last month by Milos Raonic in the third round, slumped to a 7-5, 6-4 loss in the Netherlands.
Bedene saved five break points before snatching the opening set courtesy of a break in the 11th game, before easing through the second to set up a quarter-final against Canada's Felix Auger-Aliassime.
"He was probably the better player in most of the first set, he was serving really well," Bedene, the world number 52, told atptour.com after beating second-seeded Tsitsipas.
"I stayed focused and it was good towards the end."
Tsitsipas, who won the season-ending ATP Finals last year, now has a 3-4 losing record in 2020.
In-form Russian Andrey Rublev and Gael Monfils, who plays fellow Frenchman Gilles Simon later on Thursday, are the only top-eight seeds remaining in the draw.
Top seed Daniil Medvedev lost to Vasek Pospisil in the opening round, while Italian teenager Jannik Sinner saw off Belgian fourth seed David Goffin 7-6 (9/7), 7-5.
Sinner, who won last year's NextGen Finals in Milan, claimed his first victory over a player ranked in the world's top 10.
"I feel great, especially now in this moment," said Sinner.
The 18-year-old will take on Spain's Pablo Carreno-Busta for a place in the semi-finals.
Filip Krajinovic (SRB) bt Vasek Pospisil (CAN) 6-4, 7-6 (9/7)
Andrey Rublev (RUS) bt Alexander Bublik (KAZ) 7-5, 6-3
Gael Monfils (FRA) bt Gilles Simon (FRA) 6-4, 6-1
Jannik Sinner (ITA) bt David Goffin (BEL) 7-6 (9/7), 7-5
Aljaz Bedene (SLO) bt Stefanos Tsitsipas (GRE) 7-5, 6-4