The Last Samuri battled on at the elbow but could not quite hold off the strong-finishing Mouse Morris-trained nine-year-old, who was remarkably winning for the first time over fences.
Forging on inside the final 100 yards under 19-year-old David Mullins - on his first ride in the race - the Gigginstown House Stud-owned gelding eventually crossed the line six lengths ahead of 8-1 joint-favourite The Last Samuri.
Vics Canvas was third at 100-1 and Gilgamboa (28-1) fourth.
Jockey David Mullins called it "unbelievable" as he reacted to the win.
He said: "It's unbelievable. I couldn't expect things to have gone any better, it all went to plan. I'm very grateful for being given the chance to ride this horse.
"There was one little mishap at the fourth-last, but thank god I came out (the other side). Everything went to plan really.
"Credit to Mouse, he's produced this horse without having won over fences. Then there's me, who's never even walked around the Grand National track.
"Mouse is a genius and he's the best man in the world for preparing a horse for one day.
"I'm very thankful to Michael and Eddie O'Leary (of Gigginstown) for giving me the chance.
"That's the best ride I've ever got off a horse and it's the best feeling to come back into a place like this.
"It was just brilliant."
Morris was almost lost for words after the race, but paid tribute to his late son, Christopher, who tragically died last summer from suspected carbon monoxide poisoning while travelling in South America.
Ryanair boss Michael O'Leary who owns Rule The World told Channel 4 Racing that he was "lost for words".
He said: "I am delighted for Mouse this horse has had two broken pelvises and he has brought him back each time. It was a great ride by David Mullins. I am just lost for words and that does not happen for very often."
Speaking ahead of the race AP McCoy said Saturday's event had the best ever line-up.
Ulster great McCoy - who retired last April at the age of 40 after 20 successive champion jockey titles and a record 4,358 winners - had to wait until his 15th attempt before finally winning the Grand National.
McCoy triumphed on Don't Push It at Aintree in 2010, becoming the only jockey ever to be crowned BBC Sports Personality later that year.
"It's a classy Grand National," McCoy said.
"There are a lot of good horses but Many Clouds (8-1) deserves to be the favourite - his performance (in winning) at Kelso (last month) was great and the one thing he does is he stays and stays and stays."
McCoy rode Shutthefrontdoor to fifth in his final Grand National last year.
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