While it was smooth passage for Sakkari it was rough going for Kazakhstan's Elena Rybakina, the fourth seed having to dig deep to see off determined Danish qualifier Clara Tauson 3-6, 7-5, 6-4 in a near empty Hard Rock stadium.
After splitting the opening two sets in a ragged back-and-forth contest, 2022 Wimbledon champion Rybakina finally seized control with a break to nose in front 3-2 in the third and would never let go of the lead.
Sakkari, putting the 6-4, 6-0 California drubbing at the hands of world number one Iga Swiatek in Sunday's final in the rearview mirror, was all business after having failed at the first hurdle in her last two visits to Miami.
Having collected her first WTA Tour title in Austin last month and following that up with a quarter-final run at Indian Wells, Yuan represented a potentially tricky first test for eighth seeded Greek.
But the Greek passed with flying colours, breaking her Chinese opponent five times in the 79-minute masterclass.
In other second round action, Ukraine's Anhelina Kalinina saved match point and came back from a set down to topple former-world number one Caroline Wozniacki 5-7, 7-5, 6-4.
Trailing 2-5 in the second set, Kalinina appeared to be heading for the exit but with nothing to lose, she came out swinging her racket to break the Dane as she served for the match.
The danger was far from over for the Ukrainian who faced match point on her own serve but stayed alive with a fearless forehand winner to cut the deficit to 5-4. Kalinina ended up winning five games in a row to bag the second set.
With the momentum now in Kalinina's corner, the 27-year-old poured on the pressure in the third set as she nosed ahead 5-3.
The Dane would also not go down without a fight as she survived three match points for the hold, leaving Kalinina to serve for the match.
Kalinina would need four match points to complete the comeback, securing victory on her third ace of the contest.
Next up for Kalinina is world number two Aryna Sabalenka or Paula Badosa.
All eyes will be on Hard Rock Stadium court for the first match on Friday as Sabalenka plays for the first time since the tragic news on Monday that her former boyfriend Konstantin Koltsov had died.
The former professional ice hockey player's death sent a shockwave through the Miami Open with players rallying to support Sabalenka.
Adding more drama to the second round match, Sabalenka will be going up against Badosa, one of her best friends on the Tour.
Brazilian 11th seed Beatriz Haddad Maia dropped the opening set to Diane Parry before rallying for a 3-6, 6-1, 6-4 win to reach the Miami third round for the fourth time and the third straight year.
It was the first victory for Haddad Maia over the Frenchwoman, who had won their other two meetings both on clay.
Americans Madison Keys and qualifier Taylor Townsend both enjoyed smooth passage into the third round.
Keys, who has never advanced past the quarter-finals in 12 previous tries in Miami, dispatched teenager Diana Shnaider 6-2, 6-4 while Townsend dumped Belgian 25th seed Elise Mertens 6-2, 6-2.
