The Czech star served 11 aces, nine in the first set. She broke Stosur's serve to take an early 3-1 lead, and did not face much of a challenge on her own serve, facing just four break points.
Kvitova served three aces in the game that closed out the opening set. The No. 4-ranked player in the world cruised from there.
Kvitova won the tournament in 2012 and lost to Simona Halep in last year's final.
Rybarikova broke Giorgi in the first game of the match and breezed through the first set in 34 minutes, earning another service break to go up 4-1.
The 22-year-old Italian could not solve Rybarikova's serve, failing to convert on 11 break points. The hard-serving Giorgi, ranked 38th, also double-faulted seven times while serving just two aces.
''It was very important for me to hold my serve, because I knew that she could make these double-faults, she can struggle on her serve,'' Rybarikova said. ''So I was really focusing to hold my serve.''
Rybarikova mixed up the pace throughout the match, stretching out points with slices and drop shots. That seemed to frustrate Giorgi, whose power game was not working.
''It's just a little bit that she has an A plan and no B plan,'' said the 25-year-old Rybarkova. ''She's a young player. If she's going to learn to have a B plan, I think she's going to be a very good player.''
Rybarikova, ranked 68th, becomes the lowest-ranked player to make New Haven finals, her first in a premier-level event.
She has four lower-level WTA titles on her resume, but her ranking dropped this season from the 30s into the 60s. She contends it was the result of unlucky draws, playing top-20 players such as Caronline Wozniacki, Lucie Safarova and Ekaterina Makarova in the early rounds of tournaments.
She beat this tournament's top seed, No. 2-ranked Simona Halep in the second round.
''It's not easy to beat all the top 20 players,'' she said. ''But, of course, sometimes I have to beat these players, and it was this tournament.''