Kvitova, ranked No. 4, bombarded Stosur with 11 aces, nine in the first set, improving to 5-0 against the Australian in hard-court matches.
''It was hard to pick up her serve,'' Stosur said. ''Certain big points, she'd go to my forehand, then my backhand, so that was difficult.
Kvitova broke Stosur's serve to take an early 3-1 lead, one of her four service breaks in the match. She did not get much of a challenge on her own serve, facing just four break points.
Kvitova clinched the first set with three aces in the last game and cruised from there.
''I knew that Sam would keep her eye little bit on her backhand (because) I have a left serve,'' Kvitova said. ''I was trying to mix it, as she doesn't know where it's going to be. Probably that was good idea.''
Kvitova won the tournament in 2012 and lost to Simona Halep in last year's final. But she came into New Haven having played just three times since winning her second Wimbledon title, losing in her second match in Montreal and her opener in Cincinnati.
''I think it's important to have this before the U.S. Open,'' Kvitova said. ''I'm really glad with my form now.''
Rybarikova may be in the best form of her career. The 25-year-old broke Giorgi in the first game and breezed through the first set in 34 minutes.
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 with 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,'' Rybarikova said. ''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 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 over the past year from the 30s into the 60s. She contends it was the result of unlucky draws, playing top-20 players such as Caroline Wozniacki, Lucie Safarova and Ekaterina Makarova in the early rounds of recent tournaments.
She beat this tournament's top seed, the second-ranked 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.''