The Colin Tizzard-trained seven-year-old ranged up alongside Willie Mullins' Un De Sceaux (10-11 fav) at the final fence and pulled clear on the run-in.
Fox Norton (5-2),  who also won the Melling Chase at Aintree, got home by a length and three quarters.
God's Own (7-1), last year's winner, was just half a length away in third.
The victory gave jockey Robbie Power a seventh Grade One win of the campaign.
Fox Norton has been a model of consistency since joining the Tizzard team, and was a close second to Special Tiara in the Queen Mother Champion Chase.
He was not inconvenienced by the return to two miles, with the strong pace set by Un De Sceaux and Rock The World playing to his strengths.
"Robbie was cool. He didn't get involved in any battles until he had to," said Tizzard. "The horse made a few mistakes and Robbie said he was going flat out the whole time.
"If you saw this horse on the gallops you'd never think he was a champion two-miler. Honestly, slow three-milers would beat him.
"This is why we get up in the morning and why we go looking at horses, to come and win at places like Punchestown. It's fantastic."
Asked if Fox Norton could step up in trip next season, Tizzard added: "I think there's every temptation.
"That was his minimum and if there had been a two-and-a-half-miler here he would have been in that.
"He'd get three miles, but of course Sizing John is there. I think he'd get two and a half or three."
Mullins said of Un De Sceaux: "We've had a fantastic season with him and will put him away now.
"The faster pace over two miles on better ground didn't suit him."
BBC horse racing correspondent Cornelius Lysaght
Robbie Power continues to live up to his surname in great style, adding this prize to a string of big-race success at Cheltenham, Aintree and Fairyhouse.
We've long known he's an excellent rider, but the confidence he must be feeling is being transmitted down the reins to his mounts.
Fox Norton took the notable scalp of Un De Sceaux, who has only previously been beaten in completed races in Ireland and Britain by the great Sprinter Sacre, and continues to live up to the type of expectations the Tizzard team has for him.
Meanwhile, whether it will be enough we don't know, but the second-place prize money and an earlier 1-2 means Willie Mullins put quite a dent in Gordon Elliott's lead in the trainers' championship.
Fox Norton followed up his Aintree success by beating Un De Sceaux in the Champion Chase at Punchestown on Tuesday.