Needing a birdie at the par-four 18th to avoid a playoff with clubhouse leader Young, the 39-year-old New Zealander produced the defining moments of his career. After a superb approach from 175 yards finished around 12 feet from the flag, Fox calmly rolled in the winning putt to complete a closing two-under-par 68 and finish on 10 under overall.
The victory completed a remarkable turnaround after Fox's record-equalling third-round 62 had propelled him into contention. He became just the third New Zealand man to win a men's major, joining Bob Charles and Michael Campbell, and only the second from his country to lift the Claret Jug.
"It's unbelievable, to be honest," Fox said. "I still don't know what to think. My nerves are all over the place. I'm not quite sure how I hit that putt on 18. It is a dream come true."
Young had set the target at nine under after charging through the field with a superb final-round 64. Starting the day tied for 20th, the American surged into contention with a front-nine 29 and seven birdies, but a costly bogey at the last after finding a fairway bunker left him waiting more than two hours to discover his fate.
"I thought 10 under had a decent chance," Young said. "I've played around the lead in majors enough to know that scraping out even par on a Sunday can be really difficult."
Overnight leader Sam Burns saw his hopes unravel early. After extending his advantage with a birdie at the second, the American dropped three straight shots from the fourth before recovering with 13 consecutive pars. His closing 72 left him alone in third on eight under.
The lead changed hands repeatedly throughout the afternoon as Si Woo Kim, Scottie Scheffler and Tommy Fleetwood all mounted challenges.
Kim briefly moved to 10 under after a flawless outward 32, only to fade with four bogeys over his final eight holes to share sixth place.
Scheffler recovered from a mixed week on the greens to get within one shot of the lead after consecutive birdies at the 16th and 17th, but a closing bogey dropped the world No. 1 into a tie for fourth with Fleetwood on seven under.
Fleetwood, bidding to become the first English-born Open champion since 1992, also threatened before three consecutive bogeys halted his momentum, although he finished strongly with birdies on the final two holes.
Fox briefly looked to have let his chance slip after bogeys at the ninth, 11th and 15th, but responded in champion's fashion. Back-to-back birdies at the 13th and 14th reignited his challenge before another gain at the 16th drew him level with Young.
A missed birdie opportunity at the par-five 17th meant everything rested on the notoriously difficult closing hole, where birdies had been scarce all day. Fox responded with a towering drive, a pinpoint approach and the biggest putt of his career to seal a memorable victory and cap one of the most dramatic finishes in recent Open history.
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