This article provides a general zero duality gap criterion for conic convex programs, using to this respect a generalized Courant–Beltrami penalty function. Our main theorem is formulated only in terms of the vector-valued constraint function of the program, hence holding true for any objective function fulfilling one of the standard qualification criteria of Moreau–Rockafellar or Attouch–Brézis type. This result generalizes recent theorems by Champion, Ban and Song and Jeyakumar and Li.