The Tunisian, who stormed up the rankings last year after runs to the final at Wimbledon and the US Open, sprayed 50 unforced errors and had her serve broken eight times in the 102-minute contest.
There were only flashes of the brilliant racket skills that have made her such a favourite on the WTA tour as Vondrousova matched everything Jabeur threw at her on a chilly evening on Rod Laver Arena.
Jabeur saved some face by breaking the Olympic silver medallist when she was serving for the match for the first time but Vondrousova broke straight back to move on to a third-round meeting with fellow Czech Linda Fruhvirtova (17).
Vondrousova is on the comeback trail after another of the wrist injuries that have plagued her career wiped out six months of her season last year and saw her drop to 86th in the world.
"It was very tough," she said. "Also, it was very late, so I think we were both very tired. I'm just very happy that I stayed focused and stayed in the match.
"I'm just very happy to get the win. Yeah, just stay alive."
"She's a great hitter," added Vondrousova. "I think she's playing amazing for her age also, so it's going to be tough match. I think she has nothing to lose.
"I just want to get some sleep, and we'll see how it goes."
Jabeur, who was hoping to become the first African woman and the first Arab to win a Grand Slam singles title, collapsed in tears after leaving the court.