Hebert set the clubhouse target on 22 under par after a brilliant 62, but overnight leader Wiesberger recovered from a slow start to reclaim top spot with his fourth birdie of the day on the 16th, only to bogey the 17th and then have to hole from five feet on the last to force a play-off.
The players returned to the 18th for the first extra hole and after Wiesberger two-putted for par, Hebert had a great chance to seal his first European Tour title but badly pushed his birdie attempt from eight feet.
Hebert had an even better chance to win when Wiesberger duffed his approach to the second play-off hole and then three-putted from short of the green.
However, Hebert also three-putted from 20 feet after charging his birdie putt four feet past and the pair headed back to the 18th tee once more.
At the third time of asking both players found the 18th green in regulation but amazingly Hebert three-putted again and Wiesberger just managed to coax in the winning par putt from three feet.
"I knew it was not going to come easy," said Wiesberger, who missed seven months of last season following wrist surgery. "I had a great warm up this morning and then it just got a little tough for me.
"I wasn't hitting the ball as good as the first three days and just dug in there. It was a great week for Ben, he could have snatched it off me on the first two play-off holes but I am so glad how it has turned out."
See you tomorrow ⛳ pic.twitter.com/eZpgJk9Ob5
— The Open (@TheOpen) July 14, 2019
Wiesberger's victory took him top of the Race to Dubai while Hebert at least had the consolation of sealing one of the three qualifying places for the Open Championship at Royal Portrush, with Andrew Johnston and Nino Bertasio taking the other two after finishing in a five-way tie for fourth.
Johnston, who recently opened up about the mental health struggles that followed his rapid rise to fame, surged through the field with a closing 62 and fought back tears as he spoke to reporters afterwards.
The 30-year-old's ready smile, trademark beard and nickname 'Beef' quickly made him a fan favourite and his cult status even led to sponsorship deals in the United States, including burger restaurant Arby's.
However, Johnston revealed in a recent blog on the European Tour website how he found himself crying alone in hotel rooms and unable to play competitive golf after putting too much pressure on himself to follow up his victory in the 2016 Spanish Open.
"It means a lot, it's been a tough year," Johnston said. "I was out there enjoying golf again, high-fiving the fans. It was a different kind of mindset. In the past I had put too much pressure on myself.
"I came back from America (in 2017) and finished 21st at Wentworth, 23rd in the French Open, 27th in the Open and I walked off every time disgusted with my performance. Now I look at it and think that is absolutely crazy.
"It's madness and that was the change of mindset but I didn't even realise it was happening and I was just slowly beating myself up for no reason."
Johnston was eventually persuaded to seek professional help and is on the road to recovery after working with sports psychologist Ben Davies and receiving a positive response to his blog.
"I've had a great reaction from it, some nice comments from players saying it has helped," Johnston added. "I think a lot of the guys have been through similar things which in a way is nice to hear. You don't want to see anyone down or anything like that but I'm not the only one.
"It can get tough out here, I want to do so well and win tournaments and I think the pressure I put on myself after 2016 and expectations were way too high instead of just having fun with it."