The film follows Spider-Man alter-ego Peter Parker in high school as he turns into a crime-fighting superhero. Garfield's real life girlfriend, Emma Stone, plays Parker's girlfriend, Gwen Stacy.
The story of young love helped lure female viewers, who made up 42 percent of the audience, according to Sony. Seventy-three percent of reviews compiled on website Rotten Tomatoes recommended the movie.
"This is a film that had something for women," said Rory Bruer, president of worldwide distribution for Sony Pictures Entertainment. "Gwen Stacy is a pretty strong woman in her own right, and the two of them had great chemistry on screen."
The new "Spider-Man" cost about $215 million to produce, plus tens of millions more for marketing. The film is Sony's second big-budget hit this summer, following the success of alien comedy "Men in Black 3" in May.
The studio's next major release, sci-fi remake "Total Recall," reaches theaters in August.
Last week's winner, comedy "Ted" about a man and his foul-mouthed, pot-smoking teddy bear, slipped to second place with domestic sales of $32.6 million from Friday through Sunday. Directed by "Family Guy" creator Seth MacFarlane, "Ted" has earned $120.2 million domestically since its debut a week ago.