Griekspoor reached the round of 16 after beating Miomir Kecmanovic, the tournament's top seed Alexander Zverev, and Giovanni Mpetshi Perricard in the previous rounds of the 'fifth Grand Slam' in California.
His opponent, Japanese qualifier Yosuke Watanuki, has impressed at Indian Wells after beating Alexander Bublik, Tomas Machac, and home hero Frances Tiafoe on his way to his first appearance in this stage of a masters tournament.
Rainfall caused a delay at Indian Wells Tennis Garden and pushed the match back some ten minutes - time Watanuki spent preparing even better for his Dutch opponent. The qualifier shot out the gates with a love game and went into battle with Griekspoor, who got to breakpoint twice but couldn't convert on either occasion.
The following tiebreak started in Watanuki's favour after the 349th-ranked player took the first mini break advantage on Griekspoor's first service point. After exchanging mini breaks, Watanuki took a 4-2 lead but couldn't contain a determined Griekspoor as the Dutchman rallied to five straight points and the set.
Dealing with two further delays during the match, Griekspoor fully took control of the game after fending off a break point from Watanuki before snatching the last five consecutive games on his way to the first ATP 1000 quarter-finals of his career.
The 28-year-old Dutchman will meet the winner of the meeting between Stefanos Tsitsipas - who eliminated Griekspoor at his home tournament in Rotterdam - and Holger Rune.
Last remaining Dutchman
Griekspoor is the last remaining Dutch player at Indian Wells after Botic van de Zandschulp's elimination one day earlier. Van de Zandschulp got knocked out in straight sets by the Argentine Francesco Cerundolo: 3-6, 4-6.
A valiantly fighting Van de Zandschulp took a 3-1 lead in the first set before giving up two consecutive breaks after a marathon game in which the Dutchman fended off two breakpoints.
The Dutch 85th-ranked player stayed in the fight for most of the second set before conceding his third break of the match in the ninth game, giving Cerundolo the opportunity to serve for the match. Van de Zandschulp managed to get to breakpoint and later played his way out of matchpoint, but eventually had to give in to his South American opponent after his second matchpoint.
