The 11-year-old was a 25-1 shot after finishing third in the Pertemps Final over hurdles at the Cheltenham Festival and moved into the race travelling powerfully.
He jumped the final fence in a clear lead and his pursuers never looked like bridging the gap as he galloped all the way to the line to secure a momentous five-length victory.
Balthazar King ran a fine race to finish second, ahead of champion jockey Tony McCoy aboard Double Seven.
Alvarado stayed on from a long way back to finish fourth.
Aspell, who at one stage had retired from riding, said: "It's a wonderful day, this is what we do it for.
"I've been watching the National since I was a very young boy.
"As much as you enjoy sharing everyone's success, you crave a bit too.
"To get a chance to ride in the National is a great thing, and to get on one with a chance is even better."
Aspell went on: "I was very conscious that I didn't want to be in front too soon over four and a half miles.
"He's a small horse, so he finds jumping hard enough.
"When I got a bit of daylight I knew I'd be fine because that was my only worry, a lack of daylight.
"Once he was in daylight he really enjoyed that part of the race."
There was a dramatic start to the race as Battle Group's reluctance to join the other runners led to a false start and when they were given the green light at the second attempt, the Johnny Farrelly-trained nine-year-old again stood motionless and took no part.
Last year's third and joint-favourite Teaforthree made it as far as The Chair before departing, while another to come to grief when still bowling along towards the front end was former Cheltenham Gold Cup hero and dual King George VI Chase winner Long Run.
Across The Bay led for a long way until almost being carried out by a loose horse as the field headed out for the second circuit, effectively ending his chance of victory.
Aspell took his time aboard Pineau De Re, moving stylishly into contention and never looking like being pegged back once he struck the front.
The Philip Hobbs-trained Balthazar King, winner of the cross-country chase at the Cheltenham Festival, was never too far off the pace, racing down the outside of the field and running a superb race to fill the runner-up spot.
Double Seven, saddled by former Grand National-winning trainer Martin Brassil (Numbersixvalverde, 2006), was the choice of McCoy and he was far from disgraced, beaten a little over six lengths.
Alvarado was never really in contention but flew home for fourth.
For those punters who bet with bookmakers paying out on the first five, Rocky Creek occupied that finishing berth.
All runners and riders were reported to have returned safely.
Newland, a former NHS general practitioner who trains at Claines in Worcester, said: "John (Provan, owner) is one of my oldest racing friends, we've been coming her for over 20 years, before I started training - he had horses before me and taught me a lot about it.
"For us to have one running in the National was a dream and to win it is unspeakable really.
"We have one running in a selling handicap at Market Rasen tomorrow!
"Leighton is a top-class jockey, he had a plan and delivered it superbly.
"One of the reasons I put him on the horse was because he's had a bit of a comeback season, he was second here on Supreme Glory all those years ago and I just thought maybe, with his confidence high, he could go one better."
Hobbs was gracious in defeat, and said of Balthazar King: "He's amazing, he ran well in the race last year but finished much better this time.
"When he jumped the third-last I thought he'd finish fifth or sixth, but he ran on really well and it's fantastic.
"I have enormous pride in the horse, he's one of the best, most consistent, tough horses - he tries so hard.
"It's frustrating to be second, but we'd have settled for that this morning."
Hobbs said of his other runner Chance Du Roy, who was sixth: "Going to three out I thought he had the better chance, but it was not to be with either."
McCoy said: "Martin had the horse in great form, but the ground was a fraction dead for him.
"Jumping the third-last I thought I had a chance of winning, but then I think the dead ground found him out.
"Dr Newland and Leighton are nice people and it's great for them to win it."
Alvarado's trainer, Fergal O'Brien, was proud of his stable star, who was making his first appearance since pulling up at Cheltenham on New Year's Day.
He said: "We're over the moon.
"It was a great effort to come back like that after the lay-off and all credit to the team for getting him here in such good form.
"Obviously we would love to come back and have another crack next year."
Long Run's owner, Robert Waley-Cohen, revealed his charge had suffered a minor injury but would live to fight another day.
He said: "I suppose there's France and Punchestown, but we'll have to see how the horse is.
"The jockey (Sam Waley-Cohen) is all right.
"The horse has got a bit of a haematoma on his shoulder. It's a very minor injury. It's like a big bruise. Otherwise, he's OK.
"He didn't go very far and he pulled himself up."
Jack Doyle was given a 12-day suspension by the stewards for, in their view, failing to pull up a horse who was clearly exhausted in Wayward Prince, who fell at the third-last.