The Argentine's baseline play caught the world no. 6 off guard, who never really recovered at any point during the hour and 44 minute match.
For van de Zandschulp, it is a momentous occasion as he recorded his first ever top-five win, and will be now looking to go the distance in Miami with his new found confidence.
Alcaraz registered three aces and returned four out of five break points to register a 6-0, 7-6 (7-5) victory on Sunday.
The Brit could only record three aces, and committed one double fault. He could not return a single break point.
Rublev recorded an outstanding 12 aces in the match and committed not a single double fault.
Alcaraz easily defeated a foe who was seeking his first Top 10 victory and who never really settled into the second-round match on Hard Rock Stadium.
Rublev hit a whopping 16 aces in the match and did not commit a single double fault. His win percentage on the first and second serves were 69% and 67% respectively.
Ryabkina had let a set and a 4-1 lead slip but recovered quite well to win the match and set up a last 32 tie clash against Spaniard Paula Badosa.
The former US Open champion hit 13 winners but also recorded 30 unforced errors which allowed his Italian opponent to take advantage.
With her best Miami Open performance to date, she advanced one stage further last year and reached the Round of 16.