Shubhankar Sharma continued his form in the final round to add similar 67 to his third round 67. Shubhakar shot five birdies and a lone bogey to finish with four-under-par 67 and lying at T34.
The Austrian entered the final day at The Renaissance Club with a two shot lead but found himself trailing after Hebert carded a stunning closing 62 to set the target at 22 under.
Wiesberger had edged back ahead with two to play but bogeyed the 17th in a 69 before a par on the third play-off hole handed him a sixth European Tour title.
For Frenchman Hebert, there is the consolation of a place in the field at next week’s Open Championship alongside England’s Andrew Johnston – who also carded a closing 62 – and Italian Nino Bertasio.
France’s Romain Langasque finished two shots off the lead, with Bertasio, Johnson, Andrea Pavan, Andrew Putnam and Henrik Stenson at 19 under.
Wiesberger missed seven months of last season with a wrist injury but now has two wins in 2019 and moves to the top of the Race to Dubai Rankings Presented by Rolex.
“We just dug in there,” said Wiesberger. “I would have loved to seal it off with a couple of pars coming in but sometimes it just tests you. I’m very grateful for how it turned out.
“I’ve always enjoyed coming to the links, Scottish links, and I’ve had nice success here in Scotland and it’s just really, really nice to be able to stand here with the trophy at the end of the day. It was a long day but somehow I managed.
“Being in places where you have no control over what is going to happen next all of last year makes it just a lot sweeter and you appreciate it a lot more.”
Johnston set the early target with the lowest round of his European Tour career and Wiesberger soon joined him as he pulled his second shot on the second into thick rough left of the green.
The leading group had swelled to four when Hebert added to birdies on the first, second, fourth, fifth and seventh with another gain on the tenth, and he led on his own when he holed from six feet at the par five 12th.
Wiesberger joined him at 20 under with an up-and-down on the par five seventh and from there it became an enthralling two horse race.
Another approach to around six feet at the 13th nudged Hebert ahead again but Wiesberger holed a long putt at the ninth to peg him back.
Hebert missed his opportunity at the gettable par five 16th but hit a wonderful tee shot to nine feet at the par three next to set the target before Wiesberger caught him again with a tap-in on the 12th.
An 18 foot left to righter on the 16th made Wiesberger a firm favourite but he failed to get up and and down after missing the green on the next, and holed a nervy seven footer on the last to take it to extra holes.
Both men parred the first trip up the 18th before bogeying the next, but a three putt from Hebert allowed Wiesberger to claim victory from five feet.
Langasque – already qualified for The Open via the South African Open hosted by the City of Johannesburg – made six birdies and two bogeys in a 67 for a fifth top ten of the season after regaining his card via the Challenge Tour.
Johnston revealed in last week’s European Tour Player Blog presented by Enterprise Rent-A-Car that he has been struggling with mental health issues and Beef’s qualification for The Open will delight his many legions of fans.
He got to 20 under with his tenth birdie of the day on the 16th but dropped a shot on the last, while Bertasio made five birdies and two bogeys in a 68.
Major Champion Stenson carded a 66 to finish a week in which the Swede only dropped shots on the 17th in round three with a 66, a score matched by Italian Pavan and bettered by two shots by American Putnam.
Spaniard Rafa Cabrera Bello, South African George Coetzee, Welshman Jamie Donaldson, England’s Lee Slattery and American Justin Thomas finished at 18 under.