Bullock had repeatedly said she didn't think she was going to win for the part she initially turned down, although the 45-year-old actress was a heavy favorite.
"Did I really earn this or did I just wear you all down?" she said after accepting the golden statue from Sean Penn.
"I have so many people to thank for my good fortune in this lifetime and this is a once-in-a-lifetime experience, I know."
In the closest race of the acting categories, Bullock was up against Meryl Steep in "Julie & Julia," former winner Helen Mirren in "The Last Station," and breakout stars Gabourey Sidibe of "Precious" and Carey Mulligan of "An Education" for their first-time leading roles.
In "The Blind Side," Bullock donned a frosted blond wig and a Tennessee twang to play Leigh Anne Tuohy, the real-life adoptive mother of Baltimore Ravens football player Michael Oher.
Bullock had already won the Screen Actors Guild and Golden Globe awards, and tied Streep at the Broadcast Film Critics awards. Streep also won at the Globes.
At 60, Streep is the most nominated actor, male or female, of all time with 16 nods, but she's gone home empty-handed since her last best-actress win for "Sophie's Choice" in 1983. Her other victory was as supporting actress for "Kramer vs. Kramer" in 1980.
"I look at the company I keep in this category and you can't pick," Bullock said backstage. "There's not one that rises above the others. I feel like I share it equally in five parts because we ladies need to stick together."
Bullock's Oscar triumph came a night after she won worst actress at the Razzies on Saturday for "All About Steve," a romantic comedy flop that quickly vanished at theaters in between her 2009 hits, "The Proposal" and "The Blind Side."
Bullock became the first person to win an Oscar and a Razzie on the same weekend. She was the rare A-list star who attended the show that pokes fun at the Oscars by giving out prizes for Hollywood clunkers.
"I had the best time at the Razzie," she said backstage. "It's the great equalizer. No one lets me get too full of myself."
Asked where she would put the Oscar and the Razzie, Bullock replied, "They'll sit side-by-side on a shelf somewhere, the Razzie maybe on a different shelf, lower."
Bullock's breakout role came in the 1994 film "Speed." She went on to score box office successes in "While You Were Sleeping" and "Miss Congeniality." But she also appeared in a string of duds before a supporting role in the 2004 movie "Crash" earned Bullock some of the best reviews of her career.
She attributed her victory to hanging in through good roles and bad.
"I didn't aspire to this," she said backstage, cradling her Oscar. "I was in awe of it, I admired it and I got to watch it like everyone else did. I didn't think the opportunity would ever present itself for me to rise to that occasion. This came out of left field, every pun intended."