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Alcaraz, 19, kicked off his 2023 campaign with eight wins in a row, including an Argentina Open title, before losing to Cameron Norrie in the Rio Open decider.
He has yet to drop a set at this fortnight's tournament in California, after up his opening win over Thanasi Kokkinakis with another strong showing against 31st seed Griekspoor.
The Spaniard will look to keep his strong form going when he meets Jack Draper in the fourth round, after 21 year-old Draper prevailed 7-6 (8-6) 6-2 in a battle of the Brits against Andy Murray.
Murray, who came into the match with six wins from his past seven outings, had an opportunity to take the match by the scruff of the neck but could not capitalise on a set point before going down in a tight tie-break, before Draper took charge.
California's own Taylor Fritz lived up to his fourth seeding, with the defending champion having little trouble in overcoming Argentina's Sebastian Baez 6-1 6-2, and he will play Hungary's Marton Fucsovics for a spot in the quarter-final.
Fucsovics, after upsetting 16th seed Alex De Minaur in the previous round, got the better of Slovakia's Alex Molcan 6-4 6-2.
Former world number three Stan Wawrinka showed he still has some gas in the tank after a surprise 6-2 6-7 (5-7) 7-5 triumph over world number eight Holger Rune, with the 37-year-old showing what he has learned through competing at the top level for as long as the 19-year-old Dane has been alive.
Jannik Sinner, the 13th seed, successfully navigated the challenge of veteran Adrian Mannarino for a 7-6 (9-7) 6-4 victory, Tommy Paul won his top-20 showdown against Hubert Hurkacz 4-6 6-2 6-4, and eighth seed Felix Auger-Aliassime knocked out Francisco Cerundolo 7-5 6-4.