The binary system Eta Carinae is a unique laboratory to study particle acceleration up to very high energies (VHE) under a wide range of conditions. Particles are thought to be accelerated at shocks forming in the wind collision region. Eta Carinae has been firmly established as a source of high energy gamma-rays in Fermi-LAT data over several orbits. With its highly eccentric orbit lasting 5.5 years, the periastron passage of the two stars is extremely close. This provides an opportunity to constrain the acceleration and absorption mechanisms of the system. Eta Carinae was detected above 200 GeV by the H.E.S.S. telescopes (H.E.S.S. Collaboration, 2020) based on data before and after the 2014 periastron. Unfortunately the 2014 periastron itself could not be observed by H.E.S.S. due to visibility constraints. Hence the 2020 periastron was the first periastron passage visible for the full 5 telescope H.E.S.S. array and was therefore monitored with an extensive observation campaign spanning the phase range from 0.97 to 1.05. We report the detection of a VHE signal from Eta Carinae during the 2020 periastron and describe its spectral properties together with simultaneous Fermi-LAT data. Together with previous and follow up observations, for the first time a VHE light curve spanning a full orbit is presented.