Her crowd-pleasing variety of slice, drop shot and change of pace and angle left the 2011 and 2014 champion flailing from the start as the Tunisian sixth seed raced through the first set in 22 minutes.
The ninth-seeded Czech had the briefest of recoveries in the second but it did not last and Jabeur marched on.
"It's amazing," a delighted Jabeur said in an on-court interview. "I love how Petra plays. I respect a lot what she has done for women's tennis and today to be able to win against her is huge for me."
Jabeur had to come from a set down against Bianca Andreescu on Saturday but had no such problems on a blustery afternoon as she took command from the start.
Kvitova struggled to deal with the lack of pace coming her way, while her own serves were erratic.
The fans loved the flashback that the hugely popular Jabeur brings to the table, where deception and angle can overcome sheer power, but even they seemed stunned at the one-sided nature of the match.
Kvitova briefly returned to the locker room in an attempt to reset but her radar remained badly off and she was soon 4-1 down having conceded a double break.
The Czech did, finally, string two games together but her body language suggested that she never really believed she could change the course of the match and Jabeur finished in fitting style by breaking to love.
Third-seeded Moscow-born Kazakh Rybakina, who beat Jabeur in three sets in last year’s final, went through after Brazilian Beatriz Haddad Maia retired at 4-1 down in the first set with a back injury.
"It will be a difficult match," Jabeur said of facing Rybakina. "I'm probably going for my revenge - it was a difficult final last year. It's going to bring a lot of memories.
"I'm hoping to play like today and just get the win. She's an amazing player. You can see she's like 'boom boom' all the time. There's no mercy with her so let's see what's going to happen."
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