The result gave the Premier League side six points from two games, three more than second-placed Palermo.
The Sicilians looked more likely to score in a lively opening at the Stadio Barbera, with Newcastle's defence backpedalling to clear shots by Franco Brienza and Andrea Caracciolo off their line.
In the 37th minute, however, James Milner broke down the left and whipped in a cross for Luque to head past home keeper Alberto Fontana.
Newcastle's teenage goalkeeper Tim Krul, making his debut, made a series of fine saves to keep Palermo out.
"A draw would have been a fairer reflection of the game, and a point certainly would have been welcome, but we are still on course to qualify from the group," Palermo coach Francesco Guidolin said.
Palermo, who are currently joint leaders of Serie A with Inter Milan, fielded a relatively weak team with first-team regulars Eugenio Corini, striker David Di Michele and the midfield duo of Mark Bresciano and Fabio Simplicio all absent.
However, they almost capitalised on an early counterattack when Brienza sprinted into the visitors' area and chipped Krul, only for the ball to be intercepted before it could cross the line.
Defensive errors almost cost both sides dear. Newcastle midfielder James Milner caught Palermo defender Andrea Barzagli in possession on the edge of his box to fire in a shot, which was well-saved by Fontana.
At the other end a poor backpass allowed Caracciolo to lob Krul, though once again the ball was cleared off the line.
The pace dropped slightly as the game wore on, but Newcastle sealed the points with Luque's header eight minutes before the break.
Newcastle comfortably maintained their advantage until the end of the first half, though Palermo several times went close to equalising after the interval.
Giovanni Tedesco headed narrowly wide from close range, and Krul saved twice in quick succession to block a Giuseppe Biava header and Caracciolo's shot on the rebound.
With time running out, Palermo coach Francesco Guidolin sent on Di Michele and Simplicio to sharpen his side's offensive edge, but Newcastle hung on for the win.
"We started well and missed two or three good chances. We also had a bit of bad luck. These are things that can happen when you've got a lot of first-team regulars sitting on the bench," said Guidolin.
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