Two-dimensional electron systems subjected to a perpendicular magnetic field absorb electromagnetic radiation via the cyclotron resonance (CR). Here we report a qualitative breach of this well-known behavior in graphene. Our study of the terahertz photoresponse reveals a resonant burst at the main overtone of the CR drastically exceeding the signal detected at the position of the ordinary CR. In accordance with the developed theory and extensive studies regarding frequency, polarisation and temperature, the photoresponse dependencies on the magnetic field, doping level, and sample geometry suggest that the origin of this anomaly lies in the near-field magnetoabsorption facilitated by the Bernstein modes, magnetoplasmon excitations reshaped by nonlocal electron dynamics. Close to the CR harmonics, these modes are characterized by the diverging plasmonic density of states that strongly amplifies terahertz absorption which, in turn, causes the photoresistance and photovoltage enhancement. Our results have several profound consequences for further research on nonlocal light-matter interaction at the nanoscale and revisit the role of nonlocal conductivity in light-matter interaction that was previously believed to hamper field compression and slowing of light. Our study refutes this perspective by revealing highly-confined ultra-slow plasmon modes enabled by nonlocality. Besides fundamental interest, our experimental results and developed theory show that the radiation absorption via nonlocal collective modes can facilitate strong photoresponse, a behaviour potentially useful for infrared and terahertz technology.