World number 71 Masarova converted all three breakpoint opportunities she had during the 87-minute encounter to secure her first career win over a top-10 player.
Sakkari had control as she consolidated an early break for a 4-1 lead but Masarova stormed back and won the next five games to wrap up the opening set.
In the second set, Masarova again consolidated a break for a 5-3 cushion and then, after Sakkari held serve to stay alive, closed out the encounter on her second match point with a backhand winner that dropped just inside the corner.
With the loss, Sakkari became the first seeded casualty of the US Open.
For Sakkari, the defeat marked the final blow in a disappointing Grand Slam year for her as she followed a third-round appearance at the Australian Open with first-round exits at the French Open, Wimbledon and now the US Open.