Fox then two-putted for birdie on the 17th hole as Knox made the first of his enormous putts on 18 to set the clubhouse target at 14-under, giving the New Zealander a chance to claim the title if he could make birdie on the last.
However, a second monstrous putt from Knox put the pressure back on Fox to hole out to get it to a second playoff hole.
He then saw an effort from a similar distance lip-out when they replayed the 18th to hand victory to Knox.
Fox eventually edged ahead with a birdie at the 17th, but Knox would not go away and that sensational 40-footer on the last proved good enough for a play-off after Fox missed from inside 10 feet for outright victory.
On the winning putt in sudden death, he added: "I said to (caddie) James, "well, we've already made this putt". Sometimes when I get too square with my feet, my upper body can get a little bit left and every putt I was missing was to the left.
"It was it was my time this week and I feel very lucky".
Fox played some brilliant golf over the 72 holes at Ballyliffin after taking the outright lead in day one and being in the mix all week.
"He also sent me a couple of videos of my body language after all the missed putts this week", laughed the four-time major victor.
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). "I hit the shots I wanted to down the stretch".
Defending champion Jon Rahm shot 66 to finish tied fourth with Van Rooyen, while Danny Willett continued his recovery from the depths in tied sixth spot.
"To make the Ryder Cup team you have to win tournaments", Knox said, "and this is a heck of a start". When Knox couldn't birdie the favourable par-five 17th, Fox struck, hitting the green in two and safely two-putting to take a one-stroke lead into the final hole.
Rory McIlroy finished his four-year stint as tournament host by finishing in a share of 28th place on two under par after a closing 71.