Using APEX-1 and APEX-2 observations, we have detected and studied the rotational lines of the HC₃N molecule (cyanoacetylene) in the powerful outflow/hot molecular core G331.512−0.103. We identified 31 rotational lines at J levels between 24 and 39; 17 of them in the ground vibrational state v = 0 (9 lines corresponding to the main C isotopologue and 8 lines corresponding to the ¹³C isotopologues), and 14 in the lowest vibrationally excited state v₇ = 1. Using local thermodynamic equilibrium (LTE)-based population diagrams for the beam-diluted v = 0 transitions, we determined Texc = 85 ± 4 K and N(HC₃N) = (6.9 ± 0.8) × 10¹⁴ cm⁻², while for the beam-diluted v₇ = 1 transitions we obtained Texc= 89 ± 10 K and N(HC₃N) = (2 ± 1) × 10¹⁵ cm⁻². Non-LTE calculations using H₂ collision rates indicate that the HC3N emission is in good agreement with LTE-based results. From the non-LTE method, we estimated Tkin ≃90 K, n(H₂) ≃ 2 × 10⁷ cm⁻³ for a central core of 6 arcsec in size. A vibrational temperature in the range from 130 to 145 K was also determined, values which are very likely lower limits. Our results suggest that rotational transitions are thermalized, while infrared radiative pumping processes are probably more efficient than collisions in exciting the molecule to the vibrationally excited state v₇ = 1. Abundance ratios derived under LTE conditions for the ¹³C isotopologues suggest that the main formation pathway of HC₃N is C₂H₂ + CN → HC₃N + H.