The Tunisian reached her first quarter-final of 2019 with the surprise victory over Konta, who has struggled since her run to the semi-finals at Roland Garros.
The 24-year-old Jabeur was inspired from the outset against the 14th seed, dominating on serve and keeping her opponent constantly under the cosh.
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Konta could never get a foothold in the match and lost the opening set comfortably as her opponent held serve to love.
Currently ranked at number 63 in the world, Jabeur was relentless from the back of the court and punished any mistakes from the Brit.
The way she closed out victory with an ace demonstrated how ruthless she was as Konta suffered an unexpected defeat at her home tournament.
Watch Jabeur beat Konta with match-point ace
"I think the rain brought me luck and the win," Jabeur said, who will now face Alize Cornet for a place in the semi-finals after the Frenchwoman Cornet beat China's Zhang Shuai 6-2 6-2.
"I like the way I played. I like to make crazy shots. The crowd are very fair. Konta is a great player and has inspired me in the past. I hope the crowd can come with me now."
The match also attracted controversy as it was pushed to an outside court while Guido Pella and Taylor Fritz took centre stage at a tournament which is ranked on a higher tier for the WTA than the ATP.
But the Brit was unable to prolong her stay in the tournament and has to attempt to rediscover her confidence before beginning her campaign at SW19.
Jabeur will next face Alize Cornet of France in the last eight at Eastbourne, while Konta must now re-focus ahead of Wimbledon.
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