The 42-year-old British actor portrays a charming escaped convict who terrorises a stay-at-home mom played by 44-year-old Taraji P. Henson.
The Sony drama was produced by Will Packer with Elba also serving as an executive producer and had an estimated budget of $13 million.
Number one: Idris Elba is shown from a scene in No Good Deed that finished in first place in the weekend box office
'It's the first brand-new post summer release to really catch on,' said Paul Dergarabedian, senior media analyst for box-office tracker Rentrak.
'It almost doubled its reported budget in its opening weekend with these box-office returns,' he added.
Packer produced the 2009 thriller Obsessed that starred Elba, Ali Larter and Beyonce Knowles that also performed strong at the box office.
Number two: Nathan Gamble and Cozi Zuehlsdorff are shown in a scene from Dolphin Tale 2
Elba, who starred in HBO's The Wire as a Baltimore, Maryland drug lord, has been busy lately with three films in the works, two in post-production and three more in pre-production.
The family-friendly sequel Dolphin Tale 2 with Morgan Freeman, Ashley Judd and Harry Connick Jr reprising their roles from the 2011 original came in second place with an estimated haul of $16.5 million.
Guardians Of The Galaxy loosened its grip on the box office as it slipped to third place with $8 million in ticket sales.
Going strong: Michelangelo, Leonardo, Megan Fox, Raphael and Donatello are shown in a scene from Teenage Mutant Ninja Turtles
The Marvel space adventure held the top spot for four weeks and remains the top-grossing film of the year domestically with more than $300 million collected in North America and $600 million worldwide.
Paramount's Teenage Mutant Ninja Turtles finished fourth with $4.8 million followed by the Fox comedy Let's Be Cops that earned $4.3 million.
Fox Searchlight's The Drop starring Tom Hardy and James Gandolfini in his last role opened in sixth place with $4.2 million while playing in just 809 theaters.
Last role: The late James Gandolfini and Tom Hardy are shown in a scene from The Drop
