Titans, starring Denzel Washington as a coach who helps integrate a high school football team, was the first film to break the $20 million mark in a debut since Hollow Man in August.
The reissue of The Exorcist was second with $7.4 million, losing just 9 percent of its audience in its second week. Almost Famous, director Cameron Crowe's fictionalized account of his life as a 15-year-old rock journalist, also held up well with a $5.6 million gross to place third, according to industry estimates.
Final figures were to be released Monday.
Titans, rated PG, stood out in a list of R-rated films and drew teenagers and adults alike.
"It's just a small, sweet movie," said Peter Schneider, chairman of Walt Disney Studios. "There hasn't been something [like it] in the marketplace.
"I think at the end of the day it's all about emotional content ... when you have something that's both emotional and funny and uplifting"
The movie was made for about $27 million, considered a modest budget for a big-studio picture. It packed theaters, averaging $11,367 per screen.
Two other new films did well in limited release. Beautiful took in $1.4 million on only 646 screens to tie with Space Cowboys for 10th place.
The movie stars Minnie Driver as a young mother obsessed with winning a beauty pageant.
Girlfight, the tale of a female boxer, made $210,000 on 28 screens for a per-screen average of $7,500.
Remember the Titans could be the "shot in the arm" the industry has been seeking after weeks of disappointing sales, said Paul Dergarabedian of Exhibitor Relations Co. Inc., which tracks ticket sales.
"Titans filled a void," he said. "A family film, a film that everyone could enjoy, was lacking."
Even so, the overall gross for the top 12 films was down nearly a third from the same period last year, marking the 11th disappointing week in a row.
But Titans could break the curse and lead a good fall season that will include expected hits such as Sylvester Stallone's Get Carter and Robert De Niro's Meet the Parents, Mr. Dergarabedian said.
"It takes more than one film to turn the box office around," he said.
Despite the highly publicized debate over Hollywood's marketing of violent films, they continued to score high with audiences.
The slasher sequel Urban Legends: Final Cut placed No. 4 with $4.7 million, while the thriller What Lies Beneath topped $150 million in its 11th week. Bait, The Watcher and Nurse Betty â€“ which includes a bloody scalping scene â€“ were in the top 10.
Here are the estimated weekend totals for the top 10 films:
1. Remember the Titans $21.2 million
2. The Exorcist $7.4 million
3. Almost Famous $5.6 million
4. Urban Legends: Final Cut $4.7 million
5. Bring It On $2.9 million
6. The Watcher $2.3 million
7. Nurse Betty $2.1 million
8. (tie) Bait $1.7 million
8. (tie) What Lies Beneath $1.7 million
10. (tie) Beautiful $1.4 million
10. (tie) Space Cowboys $1.4 million