Smith was just the third woman to train a National winner. Jenny Pitman was successful with Corbiere in 1983 and Royal Athlete in 1995. Venetia Williams trained the 2009 winner Mon Mome.
Auroras Encore showed stamina was his forte when he powered clear at the final fence of the near four-and-a-half mile slog and stormed up the run in to win by nine lengths.
Cappa Bleu (12-1) was second and fellow Welsh-trained Teaforthree (10-1) third. The final horse to place was another 66-1 hopeful, Oscar Time.
Fortunately, after the race had been marred by the deaths of horses at each of the last two Grand Nationals, all 40 horses and their jockeys came home safely.
"He's a grand little horse - you can ride him anywhere, anyhow," Smith told Channel 4 television of the 11-year-old Auroras Encore.
"We knew there was a strong possibility he'd get the trip. The ground was in his favour and Ryan Mania gave him a wonderful ride."
Smith, 65, trains in the Yorkshire Moors in partnership with husband Harvey Smith, a former British Olympic showjumper.
"He was just class," said Mania of the horse, who had not been amongst the favourites for the four-and-a-half mile race.
Favourite Seabass, ridden by Katie Walsh and backed by a swell of public money in expectation of a first female jockey to ride a National winner, was never a threat.
FULL RACE RESULT
1-Auroras Encore (Ryan Mania) 66-1
2-Cappa Bleu (Paul Moloney) 12-1
3-Teaforthree (Nick Scholfield) 10-1
4-Oscar Time (Sam Waley-Cohen) 66-1
13-Seabass (11-2 favourite)
14-Across The Bay
DID NOT FINISH
Fence 8: The Rainbow Hunter (unseated), Treacle (unseated), Big Fella Thanks (unseated)
Fence 11: Ninetieth Minute (pulled up)
Fence 12: Tatenen (fell)
Fence 15: Viking Blond (pulled up), Colbert Station (unseated)
Fence 17: Lost Glory (pulled up)
Fence 19: Joncol (pulled up), What A Friend (pulled up)
Fence 21: Becauseicouldntsee (pulled up)
Fence 22: Imperial Commander (pulled up)
Fence 24: Forpadydeplasterer (pulled up), Quel Esprit (pulled up), Weird Al (pulled up), Ballabriggs (pulled up)
Fence 25: On His Own (fell), Harry The Viking (pulled up)
Fence 27: Mr Moonshine (pulled up)
Fence 30: Roberto Goldback (unseated), Sunnyhillboy (unseated), Chicago Grey (pulled up), Mumbles Head (refused)