Knox holed out from nearly exactly the same distance and place for birdie before Fox saw his attempt from close range catch the edge of the hole and spin out.
The win, Knox's seventh success as a pro, will lift him some 44 spots to the new world No 43 and has seen Knox jump to fifth on the Race to Dubai.
After falling as far as No. 137 in June, Knox is back inside the top 50 for the first time since the Wyndham Championship in August. The win comes one week after a T-2 finish at the HNA French Open, and it helped the Scot jump from No. 87 to No. 49 in the latest rankings.
It was a wonderful conclusion to a tournament that was hugely successful. Like, just react.' I mean, I pured the putt. I gave myself plenty of chances and had one putt been an inch either way I'd still be out there now or even with the trophy in my hands.
Knox now has two weeks on home soil with not only the goal of a first Scottish Open triumph but matching Paul Lawrie's feat of becoming the second Scot in three Carnoustie Open's to lift the Claret Jug. That would certainly make up for his disappointment at missing the last Ryder Cup, when he came so close on his own merits, but then failed to get one of the captain's wild card picks.
'I do fancy my chances at Carnoustie, actually, but I'm not being greedy right now, ' he said. "This is a heck of a start but I feel I have more to go".
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"My goal was to come to Europe for a month and then try and win a tournament, and to finish tied second last week in France and then to win this great tournament, I feel very lucky and unbelievable".
'It's tough to describe how incredible this feels, ' said Knox, clutching the trophy proudly to his chest.
Fox and Knox looking set for two-man play-off.
Campillo sandwiched a birdie on the 13th with bogeys on the 11th and 16th but an eagle from 40 feet on the 17th had him in a share of the lead, where he was soon joined by Van Rooyen who birdied the 13th.
The only disappointment was that there was no Irish challenge near the top of the leaderboard over the last two days.
For Fox, while he will have been gutted to come up short, he's assured of a place at the Open Championship in two weeks time at Carnoustie, as will the victor. Also sharing sixth was Danny Willett (72).