David Letterman and “NBC Nightly News” anchor Brian Williams topped last night’s show with a copy of their favorite newspaper — and The Post headline proclaiming the death of Osama Bin Laden.

Letterman’s smile belies a sticky situation: his own network’s anchor, Katie Couric, has announced she’s leaving CBS. Her bosses didn’t even bother to call her in Sunday night when news of Bin Laden’s death shook the world.

So when Dave needed someone at the last minute to come on the late-night show to talk about the dead al Qaeda leader, he called Williams at rival NBC.

“Let’s hold a picture of The Post, you and I, and then it’ll be in The Post tomorrow,” Letterman joked to Williams while they posed.

You were right, Dave.