The duo entered the final day six shots off the lead but with very high winds and showers at Emirates Golf Club, the leaderboard and the event was blown wide open.
Bezuidenhout and Herbert both fired brilliant rounds of 68 to get to nine under, with the South African finding water after laying up on the last and making a clutch putt for bogey, while Herbert birdied the 17th and 18th.
It was the Australian who found the water with his second on the first play-off hole before saving par thanks to a stunning shot from the drop zone to take it back to the tee.
His second shot next time around could not have been more different, as he got within 20 feet and a two putt birdie handed him the title
With tighter fairways, thicker rough and firmer greens than in recent seasons, Emirates Golf Club produced the highest winning score in tournament history, 15 shots more than Bryson DeChambeau last season.
But that was no problem for Herbert, whose victory on Australia Day in his 50th European Tour event moves him back into the top 100 on the Official World Golf Ranking.
"It's the best thing ever, it's so good," he said. "We've got a bottle of scotch at home to celebrate back in Australia so I can't wait to get into that with the boys."
Australia continues to battle against bushfires that have brought havoc and tragically claimed lives, and Herbert had a message for all his fellow Australians.
"There's some pretty average stuff happening in Australia right now with the fires and Cam Smith said it a couple of weeks ago when he won, everyone around the world is behind us and hopefully we can keep fighting harder than what I did on that first play-off hole," he said.
"That's nothing compared to the firefighters and volunteers that are putting out the fires so i'm sending all my love back home."
While everybody else was struggling against the wind, Bezuidenhout was thriving, birdieing the par three fourth and seventh to turn in 33.
He then started his back nine by taking advantage of the par five tenth and holing a long putt from the fringe at the 11th to move into a share of second.
Overnight leader Wu chipped in for birdie on the seventh but his three shot advantage did not last for long as Bezuidenhout got up and down from a bunker on the par five 13th to move into double figures, with the 34-year-old bogeying the eighth.
Herbert was still back in the pack after an opening bogey was followed by two birdies but the leaders started moving back towards him.
Wu had to play out sideways on the tenth and three putted for a double bogey before dropping further shots on the 11th, 13th and 15th.
That left Bezuidenhout with a two shot lead in the 18th fairway but he put his third in the water to gasps of amazement from the galleries. A clutch 15 footer kept the damage to one shot as the 25-year-old set the target but the door was now open for Herbert.
He had sandwiched a bogey on the 12th with a pair of birdies and made another gain on the 17th before hitting the 18th green in two for a birdie-birdie finish and a place in the play-off.
Arnaus dropped a single shot in a 70, while Burmester got round in level par and Lewis carded a 74.