Glebova and her parents hugged and waved Canadian flags on stage -- and thanked Canada for giving them the chance to start a new life.
That's because they arrived there just 11 years ago, from Tuapse in southern Russia.
Glebova tells RFE/RL it was hard for her to adjust at first.
"There was a time [when] I was the only school student with an accent, with a Russian surname, and I didn't speak English very well. So it was difficult and embarrassing for me," Glebova says.
No longer. Almost all trace of that accent has gone, and Glebova even drops the occasional English word into her Russian conversation.
Which raises the question -- does she feel Russian? Or Canadian? Or a citizen of the world?
"I feel I'm a 'Russian-Canadian' because Canada has so many people from many different countries -- we're all Canadians, but we've all come from somewhere else. So I feel Canadian, because I consider Canada my home, it's where I live. But my Russian roots will always be in me, so I feel Russian too," Glebova says.
Glebova is not the first Russian to become Miss Universe.
Oksana Fyodorova won the contest three years ago. But she was stripped of the title, reportedly for gaining weight and refusing to fulfill her duties.
At this year's contest in Thailand, Glebova says her Russian background helped her make friends with some of the other contestants.
"I got to know a lot of the Russian-speaking girls. There were six of us, we got really close -- Miss Latvia, Miss Russia, Miss Ukraine, Miss Georgia, and Miss Israel. We plan to meet up, for sure, all our group, we're even planning a trip together, maybe to Crimea," Glebova says.
That's if she has time. As Miss Universe 2005, Glebova is expected to devote the year to charitable activities, spreading awareness of HIV/AIDS, visiting hospitals and raising money for research.
Glebova just completed a business studies course and one day hopes to own her own business, perhaps in information technology or public relations.
She's also been working as a model and motivational speaker.
And she's a trained pianist, too. "It's true I studied in music school, in Tuapse. When I came to Canada I began to learn other instruments. I played saxophone for a year, and I tried to learn to play the guitar a little. I still play the piano," Glebova says.
So could she play a duet with, say, fellow sax player, former U.S. President Bill Clinton?
"I don't think so, it was so long ago [that I played]," Glebova says.
The new Miss Universe says she also wants to use this year to be a role model for other immigrants.
Then Glebova will have one last task -- crowning her successor as Miss Universe next year.