Magic of Light was second with Rathvinden third.
There was one fatality after Up For Review fell heavily at the first fence, suffering severe injuries.
Tiger Roll, the hot pre-race favourite, owned by Ryanair chief-executive Michael O'Leary and trained by Gordon Elliott, stayed clear of trouble but made a small mistake four fences from home.
He showed his class, however, and as his rivals began to tire towards the end of the four-mile slog, he found another gear to streak home in the spring sunshine.
Red Rum, a horse which became a national icon, won in 1973 and 1974 and again in 1977.
"He's just an unbelievable horse," the 39-year-old Russell said of his mount. "I can't believe it. At my age now to win two Grand Nationals -- wow!"
Trainer Elliott could hardly contain his joy in the winners' enclosure, jumping around and hugging the horse that was bought for 10,000 pounds ($13,000) to "sell on" because he was thought to be on the slow side.
"What a horse, what a horse," Elliott said. "We worked very hard for this the whole time and I have a brilliant team behind me. Davy Russell's mum died last year and this was for her."
Elliott also trained 2007 winner Silver Birch.
O'Leary added: "It's incredible. I thought he had no chance. What a horse. He keeps improving I just don't understand him. I'm so thrilled."
(Reporting by Martyn Herman, editing by Ed Osmond and Pritha Sarkar)
