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The 25-year-old, who received a major boost by appearing at the Olympics opening and closing ceremonies last summer, also picked up the best British female artist on a night of few surprises in terms of winners and on-stage antics.
"I think I'm a very unlikely pop star," an emotional Sande told a packed O2 Arena in London on receiving the best album prize.
"This is an album I wrote because I didn't have the confidence to sing these things in person. This is a dream, really, so thank you for this year and thank you for this award. I'm so grateful."
Sande capped her success by performing a medley of "Clown" and "Next to Me" to close the ceremony, broadcast live on commercial channel ITV.
The other multiple winner was singer-songwriter Ben Howard, who picked up two of the dotted statuettes designed by Damien Hirst, for British breakthrough act and British male solo.
Among the most popular triumphs was that of Frank Ocean, American R&B star who beat acts including Bruce Springsteen and Jack White to land the international male solo artist prize.
"Before this year I didn't get me any trophies in my life and I'm definitely a long way from working fast food in New Orleans," he told the audience, referring to his humble upbringing before breaking into the musical mainstream.
Devon rockers Muse got the annual awards ceremony off to a rousing start with "Supremacy", complete with fireworks and a full orchestra standing on balconies behind them.
Justin Timberlake wore a tuxedo to perform "Mirrors", continuing his pop comeback ahead of the March release of "The 20/20 Experience", his first album since 2006.
Taylor Swift donned a white, floating gown for "I Knew You Were Trouble" before an instant change into a figure-hugging black outfit complete with skimpy shorts and knee-length boots.
One Direction received one of the loudest screams of the night as they took to the stage to sing charity single "One Way Or Another", which has reached No. 1 in 60 countries, underlining their status as global stars.
In recognition of that international reach, they were honoured with the BRITs global success award.
James Corden, the comedian hosting the ceremony, made joking reference to One Direction's Harry Styles and his highly public love life.
"Sharon Osbourne is here, Annie Lennox is here. Who have you got your eye on?" Corden asked.
Styles, seated along with his bandmates at a dinner table in a room packed with hundreds of other stars and industry bigwigs, smiled sheepishly and hid his face behind an awards program.
Robbie Williams, who has won a record-breaking 12 BRIT Awards as a solo artist, sang "Candy", and Mumford & Sons, winners of the British group award, performed "I Will Wait".
In the most hotly contested best album category, Sande had been up against Mumford & Sons for "Babel", Alt-J ("An Awesome Wave"), Paloma Faith ("Fall to Grace") and Plan B ("Ill Manors").
Sande's was Britain's best-selling album in 2012, but the ongoing slump in CD sales last year loomed over what should be a celebration of the vibrant state of the country's pop music scene.
According to official figures, overall British album sales fell 11.2 percent to 100.5 million in 2012, despite a rise of nearly 15 percent in digital album sales.
While digital downloads account for an increasing share of record label revenues, the bulk still comes from physical CDs, and the steady decline blamed on online piracy and a shift towards buying singles online is a major concern.
Adele added to her groaning trophy cabinet with the best single award for James Bond theme "Skyfall". She was in Los Angeles rehearsing for her performance at the Oscars ceremony on Sunday and so was unable to collect the trophy in person.
American singer Lana Del Rey scooped the international female award, while Coldplay pipped The Rolling Stones to the best live act prize.
Veteran rockers the Stones were shortlisted after returning to the stage for a short, sellout tour of London and the United States at the end of 2012 to mark 50 years in the business. The last time they were nominated for a BRIT was in 1996.