SEE MATCH PHOTOS
She attacked the net well and with great purpose and showed a new-found aggression to win the decider 6-4 in a match lasting one hour and 55 minutes.
Giorgi will face the winner of the match between Aleksandra Krunic or Madison Brengle in round two.
"It was a tough match, but I was pleased with my level," commented Giorgi after the game.
"I love playing at Wimbledon and coming to London - the most beautiful city.
"I am always warmly received by the crowd and it helps me raise my game."
Attention turns to Dudi Sela on Tuesday as he tackles former champion Rafael Nadal in the second match on Centre Court on Tuesday.
Diego Schwartzman is also in action, against Mirza Basic.