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.
"He's a grand little horse - you can ride him anywhere, anyhow," Smith told Channel 4 television.
"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 1,000 feet up in the Yorkshire Moors in partnership with husband Harvey Smith, a former British Olympic showjumper.
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.