"For the first time I play as if I was at home," said 20-year-old Tsitsipas, who reached the semi-finals at the Australian Open last month.
"I felt confident and I hope I will continue to show a good performance. Struff played very well but I was lucky in some of the games and it helped me a lot."
Greece’s emerging talent will meet experienced Frenchman Gael Monfils, who defeated Kazakhstan's Mikhail Kukushkin 7-5 6-3, in the quarter-finals on Friday.
Fernando Verdasco also secured his place in the quarter-finals with 6-2 4-6 6-1 win over Romanian Marius Copil.
Big-serving Copil, who reached the tournament's final last year, bombarded Verdasco with 10 aces, but had no answer to his opponent's brilliance in the final set.
"I have been able to put more returns than him in the third set," said the 35-year-old Spaniard. "I made fewer mistakes from the baseline."
Next up for the veteran is Italian Matteo Berrettini, who stunned top seed Karen Khachanov with a three-set win in the second round on Wednesday.
Russian third seed Daniil Medvedev came back from a set down to beat Dutchman Robin Haase 5-7 6-2 6-2 and book his place in the last eight, where he will face Slovakian Martin Klizan who outclassed German qualifier Daniel Brands 7-6(5) 6-4.
Marton Fucsovics also made it to the last eight after a 7-6(3) 3-6 6-4 win over another German qualifier - Yannick Maden. The Hungarian will face fourth seed Roberto Bautista Agut of Spain, who won the tournament in 2016.
(Reporting by Angel Krasimirov; Editing by Toby Davis)
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