This challenges notions of how these powerful electromagnetic rays - like light, but far more energetic - are formed, researchers suggest in Science.
They found emissions at more than 100 gigaelectronvolts - 100 billion times more energetic than visible light.
The Crab Nebula that hosts the pulsar continues to amaze astronomers, despite being one of the most studied objects.
The remnant of a supernova that lit up the skies on Earth in 1054, it has been taken in modern times to be a constant source of light - so constant that telescopes were trained on it for calibrations.
But earlier this year, the Crab was spotted emitting gamma-ray flares that have confounded astronomers.
Within the nebula lies the Crab Pulsar - a tiny, rapidly spinning neutron star that sprays highly energetic electromagnetic rays out at its poles like a lighthouse beam, sweeping past the Earth 30 times a second.
The pulsar's enormous magnetic field is known to gather up particles and accelerate them - in a process much like particle accelerators here on Earth.
As those particles move in curved paths, they emit the gamma rays that we can measure.Models re-shaped
The new find complicates the story further, because that more steady beat of pulsar emissions seems to contain higher energies than was ever expected.
Current models of this process put an upper limit on just how energetic the photons will be.
But Nepomuk Otte of the Santa Cruz Institute for Particle Physics in California said that results from the Fermi space telescope suggested the Crab Pulsar might hold a surprise.
Fermi only measures gamma rays up to an energy of 20 gigaelectronvolts (GeV), but there were hints in the data that the pulsar might have more energetic particles that were not being caught.
"If you were more optimistic, and asked yourself 'is it also possible that with these data there should be more emission above 100 GeV', the answer was a clear yes... even though the models didn't expect that," Dr Otte told theScience podcast.
So Dr Otte and his colleagues turned to the Arizona, US-based Very Energetic Radiation Imaging Telescope Array System (Veritas), which can measure far higher energies, and trained it on the pulsar.
They spotted gamma rays with energies of far more than 100 GeV, and there were further hints that there may be teraelectronvolt rays; that puts them nearly on a par with particle energies at the Large Hadron Collider.
"These are much, much higher energies than had been previously thought can come from a pulsar," Dr Otte said.
He said that there is something missing in our models of the "cosmic particle accelerators" that give rise to the gamma rays; they must arise from much further out in the magnetic fields of the pulsars.
"It's a very radical change to the picture of how we believe gamma-ray emission comes from pulsars," he said.