"The Other Woman", a comedy about three women out for revenge on a cheating husband, was second with $14.2 million, according to estimates on Sunday from tracking firm Rentrak.
In third place, faith-based drama "Heaven Is for Real" took in $8.7 million, bringing its total to $65 million, while another superhero sequel, "Captain America: The Winter Soldier", took the No. 4 slot with $7.8 million.
The big-budget "Spider-Man 2" is expected to rank as one of the year's biggest films.
Andrew Garfield returns as the superhero who swings through the skyscrapers of New York, this time battling new villains including Electro, played by Jamie Foxx.
Emma Stone portrays Gwen Stacy, the girlfriend of Spider-Man's alter ego Peter Parker.
"Spider-Man", released by Sony Corp's movie studio, kicks off a parade of action-packed superhero and monster movies that will reach theaters by August, including "Godzilla" on May 16 and "X-Men: Days of Future Past" on May 23.
"The Other Woman" stars Cameron Diaz and Kate Upton as women who are dating the same married man. Leslie Mann plays his wife.
Walt Disney Co distributed "Captain America".
"The Other Woman" was released by 20th Century Fox, a unit of Twenty-First Century Fox.
"Heaven Is for Real" was released by Sony.