For marketers of genre films, the devil is often in the details of timing — which worked out quite well last week for Paramount’s low-budget exorcism pic “The Devil Inside.” The pic debuted far better than expected — with $33.7 million — leading the first frame of the 2012 domestic box office 24% higher than 2011’s.

“Devil” is the third-highest January opening, behind 2008’s “Cloverfield” ($40.1 million) and the “Star Wars” reissue, which bowed to $35.9 million in 1997.

“Devil’s” success should bolster the trend of releasing genre films this time of year. For Par, the returns on the pic are particularly heavenly, considering the film cost only $1 million to acquire. Added to a reportedly limited marketing spend, “Devil” already is profitable.

That’s fortunate for Par because horror films typically see steep declines in subsequent frames. And “Devil” could fall even further than usual. The film received an overall F CinemaScore rating. While some filmgoers rated the pic positively (not representative in its comprehensive appraisal), most gave the pic a C rating or worse.

While “Devil” had the recent sesh mostly to itself, this week will see competition from “Contraband” and “Joyful Noise,” followed the week after by “Underworld Awakening.”

For Par, though, “Devil” has already exorcised its box office demons.