If one is inclined to entertain the notion of hurling one’s cell phone into traffic, immersing it in water, or doing whatever else it takes to make it stop delivering bad news, garbled messages, and unsolicited contact from without, “Eagle Eye,” a new thriller from Steven Spielberg’s DreamWorks creative brain trust, may be just the ticket.

Within the first reel, slacker Jerry Shaw (Shia LaBeouf) gets drawn and quartered by his phone. First, a voice belonging to Jerry’s mother delivers the worst news imaginable. Then, after returning from the funeral that prompted the call, an unidentified female voice explains to Jerry that a terrorist starter kit that’s just been anonymously delivered to Jerry’s shabby Chicago digs has come with a complimentary visit from the FBI. Clearly, Jerry might’ve done better to leave his ringer off.

Once Jerry is in FBI custody, the special agent in charge, Thomas Morgan (Billy Bob Thornton), informs him that the weapons and the $751,000 that have appeared in Jerry’s checking account just as inexplicably have changed Jerry’s job description from Xerox jockey at the local print shop (“copy associate,” Jerry incredulously insists) to traitor. Lucky for Jerry, he’s not the only one getting cranked. Across town, Rachel Holloman (Michelle Monaghan), a sterling example of the modern thriller’s ubiquitous drop-dead gorgeous unattached single mother, fields a call from the same disembodied female voice that generously offers to let her son live if Rachel does as she’s told.

Following their respective phone instructions (supported by flashing updates on any and all public electric signs and monitor screens along the way), Jerry and Rachel meet and, in spite of generating a wake of destroyed cars and public property that might even set Jason Bourne to “tsk-ing,” manage to stay a few steps ahead of the FBI and various other concerned and heavily armed agencies en route to an inevitable confrontation with the source of those annoying calls.

If, like the four screenwriters credited with penning “Eagle Eye,” you are familiar with the conventions of the post-Hitchcock “wrongly accused every-couple cross-country survival blitz” genre, there’s little coming off the page that is surprising. The identity of the female control voice and the magnitude of the conspiracy involved are, in fact, so obvious yet far-fetched that they will likely have been abandoned by most speculating viewers on grounds of stupidity a third of the way into the picture.

There is also product placement enough here for 10 films. I sincerely hope that filmmakers don’t take up the gauntlet thrown down by “Eagle Eye” and try to top the number of individual uses of the words “Porsche Cayenne,” for instance. Some records were not meant to be broken.

But, as in Mr. LaBoeuf and director D.J. Caruso’s prior Hitchcock update, “Disturbia,” “Eagle Eye” is otherwise blessed with relatively solid and sincere film craft. As the film ramps up in preposterousness and mercifully abandons a none-too-compelling fascination with electronic privacy invasion (yawn) in favor of unapologetically fanciful story material previously tailored by the likes of Ken Russell, Stanley Kubrick, and Joseph Sargent, “Eagle Eye” is actually pretty fun. The zeal with which incidental characters are dropped in their tracks in various sneakily cinematic ways, for example, at times suggests a splicing of the clubfooted Tony Scott techno thriller “Enemy of the State” with Richard Donner’s original “The Omen.”

Mr. Caruso could stand to take a page from Mr. Spielberg’s action choreography style book by including an occasional reorienting long view amid the blizzard of streaky, quick-cut action that propels the chase scenes in “Eagle Eye.” But he is a filmmaker who, unlike Michael Bay and his ilk, has a sensitivity for how stunt montages play outside of the insulated and self-congratulatory confines of the cutting room. “Eagle Eye” bears all the conceptual scars of most over-planned, under-thought, and under-felt popcorn fodder. Yet for the most part, Mr. Caruso and company meet the film’s noisy goals without being overtly insulting. In American filmmaking of any budget and artistic ambition, that in itself is a latter-day miracle of the movies.