In order to make sense of his life, a white-collar widower decides he has to tear it all down in “Demolition,” dismantling appliances, smashing furniture and even going so far as to bulldoze his own house in search of a catharsis that never comes. It all could have gone horribly awry, were it not for the top-of-their-game contributions of leading man Jake Gyllenhaal (continuing in recent-streak crazy mode) and director Jean-Marc Vallee (back in early-career “C.R.A.Z.Y.” mode), whose unexpected creative choices across the line salvage a sledgehammer-obvious screenplay that will stop at nothing to provoke a reaction. Though dated to open after the Oscar dust has settled with an April 8 release, Fox Searchlight might rethink that strategy if reactions to this alternately tough and ingratiating Toronto opener are strong enough.

Featuring the most baldly manipulative first and last five minutes of any movie this year, “Demolition” opens with Wall Street slimeball Davis Mitchell (Gyllenhaal) and his wife, Julia (Heather Lind), bickering in traffic when a car blindsides them mid-thought, jarring both the Mitchells and the audience — an increasingly prevalent and virtually inexcusable tactic whereby any dialogue set in a moving vehicle and shot head-on becomes a chance for directors to catch us off-guard. That very same emotional shock ploy was used twice at Cannes, in “The Sea of Trees” and “Chronic,” and it’s high time we gave this stunt a name, so Variety hereby proposes calling it “a Demolition,” as in, “The couple were driving along, talking about fixing the refrigerator when the director pulled ‘a Demolition,’ and the next thing we know, we’re in the hospital and the wife is dead.”

Theoretically speaking, an opening like that should put audiences on edge for the rest of the movie, leaving us constantly jumpy about what might come next, and sure enough, though Bryan Sipe’s screenplay is shameless when it comes to beating its metaphors, one could hardly accuse it of being predictable. That’s instantly clear in the way Davis processes his wife’s accident — or rather, how Vallee approaches the critical, tone-setting scenes that immediately follow. Treating Julia like a ghost (the way he did Laura Dern’s dead mom in last year’s “Wild”), the helmer uses jump cuts and poignant dips-to-black to convey the numbness the character feels in place of grieving.

While his father-in-law-cum-boss, Phil (Chris Cooper), stays home wracked with guilt, Davis goes back to work almost immediately. He clearly needs someone to talk to, but rather than turning to anyone familiar, he composes a long, brutally candid letter to the company responsible for stocking the candy-withholding vending machines in the ER under the pretext of asking a refund. At first, this epistolary therapy seems like little more than a device to get Gyllenhaal’s character talking: The film has a fair amount of exposition to unload, and this is a relatively novel and quirky way to do it. Besides, Davis is obviously suppressing his own reaction to the accident and needs an excuse to get in touch with his feelings.

But these letters play a more substantial role than that, seeing as how Sipe actually follows through on his weird creative choice and invents a woman on the other end of Davis’ letters: Champion Vending Machines customer service rep Karen Moreno (Naomi Watts), who is so moved by the correspondence that she decides to call Davis at 2 a.m. to offer a sympathetic ear — which is all he ever really needed. Karen is drawn in because she’s never met anyone as honest as Davis, and Davis is happy because he finally has someone who will listen, although befriending Karen comes with the added challenge of dealing with her rebellious long-haired son, Chris (Judah Lewis), who really loves classic rock.

As it happens, so does Vallee, who notoriously deferred his director fees on “C.R.A.Z.Y.” in order to secure the David Bowie and Rolling Stones songs he wanted on that soundtrack, and who pumps up the volume here every chance he gets, blasting everything from Mr. Big’s “Free” to Heart’s “Crazy on You” to help throttle Davis out of his funk — quite literally at one point, as Gyllenhaal dances along to his newly upgraded playlist through the streets of Manhattan. Chris’ character could be a reincarnation of (or at least soul brother to) the gay, music-driven protagonist of the beloved coming-(out)-of-age pic that put Vallee on the map, and “Demolition” benefits from a comparably cheeky, dramedy-defying approach to material that might have played as either flat or overly precious in another director’s hands.

That doesn’t necessarily excuse the fact that Sipe’s script seems to be working overtime to jerk tears. Just because Davis doesn’t feel anything for his wife’s loss doesn’t mean we won’t, either, and it’s hard to watch the red-eyed Cooper without welling up ourselves, especially considering how stoical the actor is in nearly everything else. Ultimately, “Demolition” falls into that category of movie about people who just need to feel something — an increasingly common zeitgeist-channeling genre led by films such as “American Beauty,” in which relatively privileged suburban white people need something to penetrate the numb discontent of their lives.

Coincidentally, Cooper played a catalyzing force in both films. Here, his character tells his seemingly unfeeling son-in-law, “If you want to fix something, you have to take it apart and put it back together” — advice that Davis opts to take literally, first with his toolbox and later by quitting his cushy nepotistic job and joining a wrecking crew. Here, it’s stepping on a rusty nail at a (de)construction site, in lieu of a windswept plastic bag, that serves as our protagonist’s wake-up call to all that life has to offer, but the message is the same. But Sipe smugly refuses to stop there, throwing a gay bashing, a surprise pregnancy and an eye-rolling and totally out-of-character 11th-hour act of charity into the mix — not to mention an astonishingly reckless scene in which he hands Chris a handgun and invites the kid to shoot him.

Somehow, amid this erratic roller-coaster of behavior, Gyllenhaal grounds Davis’ wildly unraveling psyche, finding both humor and heart in a man who admits to having spent the past 10 to 12 years incapable of feeling. Considering how far the dedicated actor will go to transform himself into someone new, famously bulking up (as in “Jarhead” and “Southpaw”) or slimming down (a la “Nightcrawler”) as the role requires, it’s doubly impressive to see him build a character without the crutch of a total physical reinvention — which is to say, that he can show up as the Jake Gyllenhaal fans know and love, and yet still disappear completely behind his own facade.

The actor reveals a near-sociopathic deadness to Davis in the early stretch, an almost Patrick Bateman-level lack of empathy when faced with the genuine grief of those around him (which also happens to be where Sipe’s quippy script works best, landing laughs at seemingly inappropriate moments), though the character gradually opens up in Karen and Chris’ company. If Davis’ “thing,” according to those around him, is an unfiltered and frequently tactless compulsion to speak the truth, then the Morenos serve as the mirrors who remind him of who he truly is, and Watts is wonderful in a rare supporting part that allows her to reflect her co-star’s soul without having to use sex in the process.

The object here is clearly to rip Davis apart and rebuild him from the pieces, and that’s a job neither he nor Gyllenhaal can pull off alone. It takes Karen’s empathy, Phil’s understanding, Chris’ wild taste in music and the ever-surprising Vallee’s mastery of tone to construct such a well-rounded character, and though “Demolition” very nearly blows it with two badly executed last scenes, the result is the best Gyllenhaal performance since “Brokeback Mountain” and a partially heartless character who manages to work his way into ours.