In “Safety Not Guaranteed,” a spirited little movie that won a screenwriting prize at the Sundance Film Festival in January, a magazine writer (Jake M. Johnson) and his two interns (Aubrey Plaza and Karan Soni) are assigned to write a feature story on the man who placed a classified ad looking for someone to travel back in time with him. (“I’ve done it before,” the ad reads. “You’ll need to bring your own weapons. Safety not guaranteed.”)

He turns out to be Kenneth (Mark Duplass), a grocery store clerk with a head filled with conspiracy theories. Kenneth is convinced he’s being followed; he lives out in the sticks in a house filled with junk. One of the most refreshing things about “Safety Not Guaranteed,” which marks the film debuts of writer Derek Connolly and director Colin Trevorrow, is what doesn’t happen next. Connolly was inspired to write the movie by a real classified ad, but he uses the idea as a springboard for a much more interesting and moving story than that set-up promises.

In her first starring role, Plaza steps away from her amusing “Parks and Recreation” schtick (the vaguely irritated young woman who always seems to be harboring a secret) and reveals a subtler, more vulnerable persona. As Darius, the intern who makes contact with Kenneth and slowly gains his trust, Plaza plays up her character’s insecurities and mild depression. She still lives at home with her father; she can’t land a real job and isn’t comfortable enough with herself to even contemplate dating. While Kenneth is looking to travel to the past, Darius is stranded in time.

“Safety” gives each of its three protagonists their own adventure. Johnson is excellent as the cynical reporter and former playboy whose vanity is about to be shattered, and Soni is quietly endearing as the nervous virgin who prefers to veg out on his computer.

But this is ultimately Plaza’s movie. Duplass keeps us guessing as to just how crazy Kenneth is. Watching Darius slowly realize she’s falling for this peculiar man, even though he’s obviously not quite right in the head, shows us a side of this gifted actress we’ve never seen before.

“Safety Not Guaranteed” is droll and hilarious, but there isn’t a cheap laugh in it, and the ending is so perfect, it just sends you soaring.