The second-place finish qualified the 31-year-old Kiwi to participate in the next major, the Open Championship at Carnoustie from July 19-22, and he also pocketed a career-best payday of €665,614 (NZ$1.14 million).
Incredibly, Knox had hit a near-identical shot on the same 18th hole to finish off his round initially.
That putt got Knox through the back door into the playoff where he holed a putt from basically the exact same spot for another birdie and his first victory non-WGC victory on the European Tour.
Fox left himself a putt to win it. He played some magnificent golf but his putter was stone cold and he will head to Carnoustie desperately hoping to rediscover his touch on the greens.
"All the bad moments are taken care of with putts like that", Knox said.
Fox birdied the 12th and put his third to three feet on the par five 13th to lead by two but he bogeyed the next, with Knox joining him at the top after a tap-in at the 15th. I've done it before in the USA on the last hole, 12 feet.
"After the eagle on the fourth, I knew I was in it because I hadn't really missed a shot", Knox said. "I hit the ball the best I've hit it on Thursday and I felt like I sort of kept it up". Then I just blacked out to be honest. 'I got to 18th in the world and I saw how good the players were around me. I read the putt and I was like, just don't aim. The way I managed to do it, holing those two long putts, it was just my time.
"I said to James (caddie James Williams): 'Well, we've already made this putt so it can't be too hard'".
China Shares Drop, Yuan Falters on New U.S. Tariff Threats
That prompted fears Beijing might go beyond matching USA import tax increases by harassing American companies in China . China has vowed to retaliate dollar-for-dollar to any further US tariffs.
"It was it was my time this week and I feel very lucky".
"I am not being greedy".
But it was Knox, who holed from 40 feet in both regulation and on the first extra hole, who hoisted the trophy though Fox claimed the consolation prize of earning a berth in the upcoming Open at Carnoustie. "I hit two great putts on 18 and one grazed the edge and one came back at me".
"I'm happy", added Fox.
Spain's Campillo finished just a shot outside the play-off after a closing 65, with compatriot Jon Rahm putting up an incredible defence of the title. "Prepare the way I normally do and go out and play and see what happens".
The Holywood man had 124 putts for the week - 24 more than he had when winning the Arnold Palmer Invitational in March.
It was a fantastic final day in front of a massive crowd.
"I feel all right", said Fox after his playoff defeat. I need to keep going and press on for the rest of the summer'.