The film, produced by JJ Abrams, went straight to Netflix without being released in cinemas first.
Filmmakers often use the highly prized Super Bowl ad slots to flag up future releases, but this is the first time the whole film has been released, industry watchers said.
Third in the series
Mission Impossible: Fallout, the next version was advertised during the game alongside a trailer for Solo: A Star Wars Story, with the full-length version set to arrive on Monday.
The Cloverfield Paradox is the third movie in the Cloverfield series, but has been in production since 2012.
Its release had been repeatedly postponed until Sunday night, when the entire movie surfaced on Netflix just a couple of hours after the first trailer.
Paramount made the film but there were reports Netflix had acquired it last month.
The Cloverfield Paradox is now available to stream on Netflix.