The pair were tied on 14 under after 72 holes at Ballyliffin Golf Club in County Donegal.
Knox holed from 40 feet for a birdie on the final green in regulation to sign for a 66 and set the clubhouse target.
New Zealander Fox put his approach into the 18th to ten feet but he missed his putt for the title, leaving the pair walking back to play the 18th again.
Knox put his second shot in a position almost identical to the one he found on the 72nd hole and rolled it home again, with Fox missing his own birdie attempt from 12 feet.
Knox said at the presentation ceremony: "It's why I play golf, all the practice, all the misses, all the bad moments are taken care of with putts like that.
"Making two of them from an almost identical position is obviously a bit of a bonus. I'm so happy. I said (on the play-off hole) we've already made this putt, it can't be too difficult. I feel bad for Ryan but I guess it was my time."
Knox, winning his second European Tour title, arrived in Ireland in good shape after finishing second at last week's French Open.
He was going one better after taking second to Irish Open host Rory McIlroy in this event in 2016.
Spaniard Jorge Campillo finished one shot out of the play-off after a closing 65, one shot clear of countryman and defending champion Jon Rahm and overnight leader Erik van Rooyen.
While he may have missed out on the title Fox gained a significant consolation prize with his strong showing earning him a place at the British Open.
The other two places for Carnoustie on offer to top 10 finishers not already qualified went to Andy Sullivan of England and South African Zander Lombard.
South African Van Rooyen entered the day with a four-shot lead and while he birdied the fourth, bogeys at sixth, seventh and ninth meant he had been caught by Campillo at the turn.