The Crab nebula displayed a large γ-ray flare on September 18, 2010. To more closely understand the origin of this phenomenon, we analyze the INTEGRAL (20-500keV) and Fermi (0.1-300GeV) data collected almost simultaneously during the flare. We divide the available data into three different sets, corresponding to the pre-flare period, the flare, and the subsequent quiescence. For each period, we perform timing and spectral analyses to differentiate between the contributions of the pulsar and the surrounding nebula to the γ-ray luminosity. No significant variations in the pulse profile and spectral characteristics are detected in the hard X-ray domain. In contrast, we identify three separate enhancements in the γ-ray flux lasting for about 12h and separated by an interval of about two days from each other. The spectral analysis shows that the flux enhancement, confined below ∼1GeV, can be modelled by a power-law with a high energy exponential cut-off, where either the cut-off energy or the model normalization increased by a factor of ∼5 relative to the pre-flare emission. We also confirm that the γ-ray flare is not pulsed. The timing and spectral analysis indicate that the γ-ray flare is due to synchrotron emission from a very compact Pevatron located in the region of interaction between the pulsar wind and the surrounding nebula. These are the highest electron energies ever measured in a cosmic accelerator. The spectral properties of the flare are interpreted in the framework of a relativistically moving emitter and/or a harder emitting electron population.