Hollywood long ago ceded “love that stands the test of time” to the realm of science fiction and fantasy, so “The Age of Adaline” falls neatly into a genre that includes “The Time Traveler’s Wife,” “About Time” and even “Somewhere in Time.”

But building this film around all the willowy, world-weary grace that Blake Lively can muster pays off. As a twenty-something who stopped aging 80 years ago, Lively suggests several lifetimes of experience in a love story that ranges from wistful to hopeful, a romance whose female half understands its consequences.

A pedantic narrator introduces Adaline under “her current alias,” Jenny, on New Year’s Eve 2014, then backtracks to give a quasi-scientific explanation to the aging that stopped after an icy car wreck in the early 1930s.

Widowed with a child, she begins to draw attention for her agelessness from law enforcement (in the paranoid McCarthy era). We watch her go underground — changing names, changing jobs, investing her money in long-shot stocks so that she’s never pressed for cash.

Now she works in the San Francisco city archives, and she and her retirement-age daughter (a sparkling Ellen Burstyn) are the only ones who know her secret.

Then a rich do-gooder of a suitor, Ellis (Michiel Huisman), fixes his eye on her. And her many polite rebuffs fail to deter him. Reluctantly, she falls for him.

The script cleverly has Adaline/Jenny catch herself, blowing off a come-on as something she first heard “from a young Bing Crosby … type.”

Then Ellis gets a line that works. He quotes Leigh Hunt’s poem “Jenny Kiss’d Me.”

Say I’m weary, say I’m sad. Say that health and wealth have miss’d me.

Say I’m growing old, but add, Jenny kiss’d me.

And for an hour, “Adaline” is warm and charming, with a somber edge. She has buried generations of spaniels. She can’t bear to bury another lover.

Harrison Ford shows up for the third act as he and the ageless Kathy Baker play Ellis’ parents. In a performance as affecting as any he has ever given, Ford lifts this romance in ways we never see coming.

But it’s Lively’s show, and she wears the period clothes and formalwear as easily as Adaline wears the burden of a body that never ages, even as the memory never forgets history learned, a language mastered or what love felt like when you last let yourself experience it.