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.
Lehecka won easily in 63 minutes thanks to his strong groundstrokes and willingness to attack whenever he could.
Mertens had only ever won once before in the second round of the 2017 New Haven tournament, giving Kasatkina a 4-1 head-to-head advantage.
Swiatek was the top seed in Miami, and after receiving a first-round bye, she was scheduled to face American Claire Liu in the second round.
The 2021 finalist Andreescu won their first-round match in Rome last year after Raducanu withdrew due to a lower back injury while trailing 6-2, 2-1.
The 2019 Monte-Carlo semifinalist defeated Murray in their first career meeting to earn his first victory on a hard court this year.