Gaga collected awards for best international female artist, best international breakthrough act and best international album for The Fame.
The singer, wearing a towering white wig, lace veil and eyelashes, paid tribute to McQueen as she collected her first prize – referring to the designer by his given name Lee.
“Thank you to Lee McQueen,” she said.
Gaga recently wore McQueen’s lobster claw shoes in her Bad Romance music video.
The designer was found dead last week after apparently committing suicide.
Picking up the award for best album, a tearful Gaga said: “I was really excited to win the first two awards. This award means even more to me because I worked so hard on this album for so long.
“My fans were the first people to believe in me. Thank you so much.”
The BRITs are the British equivalent of the Grammys, with most winners selected by a vote of more than 1,000 industry members.
US rapper Jay-Z claimed the award for best international male during the ceremony at London Earl’s Court arena.
British boy band JLS won the award for best domestic breakthrough act, while Kasabian were named best British band.
Florence And the Machine picked up best British album.
Dizzee Rascal walked away with the best British male solo artist award, while Lily Allen won the female equivalent.
Recently-split rockers Oasis won a one-off prize – their (What’s The Story) Morning Glory? was named best British album of the last 30 years.
The Spice Girls were recognised for the best BRIT Awards performance of the last 30 years for 1997’s Wannabe.
Former Take That member turned solo artist Robbie Williams, meanwhile, received a special award for his contribution to music.
“Yeah, I’ve chipped in,” Williams joked. “Odds and sods over the years.”