In this letter we report the first multi-differential measurement of correlated pion-proton pairs from 2 billion Au+Au collisions at √ s N N = 2.42 GeV collected with HADES. In this energy regime the population of ∆(1232) resonances plays an important role in the way energy is distributed between intrinsic excitation energy and kinetic energy of the hadrons in the fireball. The triple differential d 3 N/dM π ± p dp T dy distributions of correlated π ± p pairs have been determined by subtracting the πp combinatorial background using an iterative method. The invariant-mass distributions in the ∆(1232) mass region show strong deviations from a Breit-Wigner function with vacuum width and mass. The yield of correlated pion-proton pairs exhibits a complex isospin, rapidity and transverse-momentum dependence. In the invariant mass range 1.1 < M inv (GeV/c 2 ) < 1.4, the yield is found to be similar for π + p and π − p pairs, and to follow a power law A part α , where A part is the mean number of participating nucleons. The exponent α depends strongly on the pair transverse momentum (p T ) while its p T -integrated and charge-averaged value is α = 1.5 ± 0.08 st ± 0.2 sy .