Sizing John, given a superb ride by Robbie Power, who had convinced Harrington he could stay further than two miles, seized the initiative at the penultimate fence to come home clear of Minella Rocco with long-time pacesetter Native River third.
He has come second twice, including a year ago after a nightmare build-up.
Willie Mullins, five times the leading Festival trainer, is still to win the Gold Cup, with favourite Djakadam finishing fourth.
Last year Kelly became the first woman to ride the victor of a Grade One jumps race in Britain, and the talented jockey has already won seven races this season.
With Sizing John she has completed the triple crown of Cheltenham's great championship races, and typically she instinctively handed the credit to Power.
Sizing John's win is rich reward for the Potts, who have poured money in to jumps racing with fervour for the past 12 years. "He jumped like a buck and it's his jumping that got him there the whole way", she said.
"He was awesome. It's thanks to Robert really--he's the one who said at Christmas, "he will stay".
Power, who won the Grand National on the Gordon Elliott-trained Silver Birch in 2007, said: "Unbelievable, Jessica Harrington is a genius".
"I still can't believe it", said Harrington.
"When I won the Grand National I was 25 and thought I was going to win everything - now I am 35 and realise I am not going to win everything so to win a Gold Cup is fantastic".
Sizing John - What's in a name?
It looks very much like it could be third time lucky for the eight-year-old who looks to be the flawless age and candidate to win a Gold Cup which is obviously missing a few high-profile stars. But I had a lot of confidence in this horse.
"You'd be disappointed if a Gold Cup victor left your yard but I'd be delighted for the horse and his connections - and my wife and I who bought him".
The Gold Cup is always a special day in the racing calendar, and this year has been no different.
Harrington started out as an worldwide eventer and rode in two Olympics before she switched to racing in 1989 and since then she has saddled a long line of top hurdlers and two-mile chasers.
Djakadam has been backed down to 11/4 ahead of the race at 3.30pm.
Won Festival race - Ryanair and come second in the Arkle.
Jockey Ruby Walsh and trainer Willie Mullins are looking to lead the horse to victory How is Djakadam's form? In so doing, he claimed his sixth victor of the week to tie with Mullins but he won the title on countback to placed runners.
One more tremendous leap was just what the doctor ordered and the seven-year-old's huge stride carried on his momentum up the famous hill.
"I was a passenger all the way", declared Johnson, who sealed the sole win of the week for west country trainer Philip Hobbs in the colours of JP McManus.
Death Duty should go off favourite in the Albert Bartlett.
Defi Du Seuil looks a real class horse. Their son, France's reigning champion jockey Pierre-Charles, couldn't make it to Cheltenham as he was too busy riding a victor at Fontainebleau only seconds before Defi Du Seuil struck at Cheltenham. "We've had another good Festival, with no complaints".
"His family traces back to my late husband's parents' bloodlines".
"He wears his heart on his sleeve and we are so proud of him".
It followed their Coral Cup victory with Supasundae on Wednesday.