HILLARY Clinton performed brilliantly in her “Late Show with David Letterman” appearance Wednesday night, making it the first brilliant — or even marginally intelligent — act of her Senate candidacy.

The key words here are “performance” and “act.” She was relaxed, smiling and amused and oh, so well prepared, as ready with soundbites and one-liners as any comedienne facing Dave in the hot seat. True, her first joke bombed — something about how the only trouble with her Chappaqua move-in was “when the satellite truck ran over the welcome wagon” — and it brought the only needling of the night from Letterman, who said: “Somebody’s been writing material for you, haven’t they?”

Yes, Dave. Only that “somebody” was you.

The “satellite truck” line might have been supplied by one of the Democratic Party’s joke writers-for-hire, like Mark Katz, or even by Hillary’s Hollywood buddy Linda Bloodworth-Thomason. But “Late Night” producer Rob Burnett acknowledged that his show’s staff helped to punch up Hillary’s material, including her supposedly self-drafted Top 10 list about why she had decided to appear on the Letterman program.

Not only that, she was also tipped off about Letterman’s “surprise” pop quiz on New York state. “Oh, boy,” Hillary said when Dave pulled out the quiz, acting nervous as only a cheater could before displaying a ludicrous amount of knowledge about the state bird (“I know that, it’s the bluebird”) and the state tree (she cleverly went through a few different maples before settling on the sugar maple). This is the sort of trivia unknown to all but a few dozen of the state’s 18,175,301 residents, but it did make Hillary sounds like she’s getting to know New York pretty well.

Letterman is an entertainer, not an ambush interviewer, and his show is intended to amuse folks as they fall asleep, not to catch Hillary Clinton out in lies and deceits. Still, Letterman and Hillary may have stumbled into sensitive territory with this mini-version of the 1950s quiz-show scandals.

Imagine, for a moment, how differently things would be for George W. Bush if he had gotten the answers in advance on that pop quiz to which he was subjected by Boston TV reporter Andy Hiller. Bush was asked questions by Hiller that almost nobody except the president of the Council on Foreign Relations could have answered off the top of his head. Yet the Republican presidential front-runner’s inability to name the rebel president of Chechnya, or the prime minister of India, inaugurated a spate of stories and jokes questioning his intelligence.

Indeed, Letterman went after Bush for exactly this reason in his No. 1 entry on Wednesday night’s “Top 10 Things a Dumb Guy Would Ask Hillary Clinton”: “Have you ever met my dad, George Bush?”

Bush may be a lightweight; the jury is still out — but then the jury is also still out on just how clever Hillary Clinton really is. Don’t forget — never forget — clemency for the FALN terrorists, kissing Mrs. Arafat on both cheeks after the blood-libel accusation, blaming Bill’s hanky-panky on fights between his ma and grandma, or her outrageous claim to be a lifelong Yankee fan.

And the fact that she cheated on the Letterman quiz offers a reminder to New Yorkers of the way she plays it fast and loose. A woman who once made a $100,000 profit in a commodities flip should not be cutting corners on national television, especially not at a time when the nation’s TV viewers are watching ordinary Joes trying to answer enough questions to get a million bucks out of Regis Philbin.

A hard look at the results of the Marist College poll on the New York Senate race reminds us anew what a terrible candidate Hillary has been so far.

When her gavotte with New York started a year ago, 52 percent of registered voters said they would cast a ballot for her as against Giuliani’s 42 percent. By July, she had dipped to 41 percent and has stayed there, while Giuliani has risen to 49 percent and has basically stayed there.

Her numbers haven’t improved, nor have Giuliani’s fallen, even during the relentless effort to give him a black eye for his homeless policies over the past two months. The only moment besides the bad joke during which Hillary showed poor judgment on Wednesday night was in choosing to attack the mayor directly on that issue instead of keeping things light and airy when she said that “as senator you can’t arrest a homeless person.”

That line probably tickled Mary Brosnahan and the city’s other homelessness mau-mauers no end, but will do little to rally support for Mrs. Clinton with the relatively tiny 11 percent of New Yorkers who profess themselves as undecided between her and the mayor.

Mrs. Clinton had a good night. But her campaign is still in crisis. It’s flatlined, like a dead patient on a hospital monitor, and the Letterman appearance wasn’t quite the shot of adrenalin straight into the heart that Mrs. Clinton needed to get her campaign to show some life again.

Next time, she should try not cheating. But then, her name wouldn’t be Hillary Clinton, would it?

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John Podhoretz’s column appears Tuesdays and Fridays. E-mail: podhoretz@nypost.com