Watching a couple duke it out works only if you also understand what drew them to each other in the first place. But in the new Broadway revival of David Hare’s “Skylight,” the lovers don’t share much, either in love or war.

It’s a cold night when Kyra (Carey Mulligan) opens the door to her rundown flat to find her ex-lover, Tom (Bill Nighy). His wife, Alice — the one he cheated on with Kyra — has died a year before, and he’s come to talk and maybe rekindle the flame.

He finds no better way to do that than unleash a stream of sarcasm, much of it directed at Kyra’s digs.

“Put a bucket in the corner to s - - t in, and you can take hostages and tell them this is Beirut!” he says.

The line gets a laugh because Nighy delivers it with delectable nonchalance, but Tom’s snobby attitude soon gets tiresome. He even nitpicks Kyra’s Bolognese sauce — which Mulligan spends a chunk of the first act preparing, chopping vegetables and seasoning meat whose aroma wafts through the theater.

Then again, Tom’s much older, a dapper restaurateur who hired Kyra when she was just 18. After they split three years ago, she went on to teach high school in a hardscrabble part of London.

The imbalance of power between them is a key part of the play, and much of that is due to their age difference: Kyra’s meant to be just north of 30 and Tom about 20 years older.

But in this production, directed by Stephen Daldry (“The Audience”), the gap has turned into a chasm: There’s no getting around the fact that Mulligan is 29 to Nighy’s 65. Indeed, Tom’s rebellious 18-year-old son, Edward (Matthew Beard) — who also drops into Kyra’s flat that day, unannounced — is closer to her age than Tom is. The lack of sexual chemistry between them makes you wonder why Kyra bothers to put up with Tom. It doesn’t help that Nighy, who first played the role in 1997, turns on the charm so hard that all we see are mannered tics.

In contrast, Mulligan is a marvel of quiet strength. She’s been very good in movies such as “An Education” and “The Great Gatsby,” but she truly comes alive onstage. And she does it in such an understated manner that it’d be easy to miss how rich her performance is.

Kyra merely listens to Tom at first, but then she turns the tables and makes a case for her beliefs and integrity against a man who dismisses them. “I still love you,” she admits. “I loved you more than anyone on Earth. But I’ll never trust you, after what happened.”

She’s done, but stronger, more open to life. In the end, it seems the show’s title refers to Mulligan’s Kyra: the one who lets in the light.