In only her second tournament back from a three-month spell on the sidelines with a wrist injury, Giorgi had no answer to the power of the Ukrainian in the Ladies Singles' match on Court Eight.
Try as she might, the Italian, 27, came out second best in a battle of the baseliners.
This was a performance littered with errors by Giorgi who had reached the quarter-finals at SW19 last year.
The world no. 42 produced 26 unforced errors and eight double faults in a match that finished 3-6, 3-6 in favour of Yastremska.
A disappointed Giorgi said: "I did not play a good match, but it was not easy coming back from a long injury.
"Last year I played with more control and a better rhythm.
"I know my game and am confident I can return to the top 20 soon."
Two more Jewish players are in action on Tuesday, with Diego Schwartzman of Argentina and qualifer Noah Rubin in action in the Men's Singles.