The recently introduced effective-gluon (EG) model is applied to inclusive meson production at large transverse momentum (p⊥) from π+/-p and pp interactions. In the EG model the dependence of the inclusive differential cross section on p⊥ and center-of-momentum energy s is characterized by a single universal constant B = 18 GeV2; this constant is obtained by fitting to the inclusive data for pp-->cX with c = π+/-, π0, K+/-, p, and p¯. Since the EG model requires that the inclusive differential cross sections for π+/-p-->cX should be characterized by the same constant B, the dependence of these cross sections on p⊥ and s should follow from the previous analysis of pp-->cX without the introduction of any additional parameters. The only new information required is the form of the momentum distribution function for partons in the incident pion. Several models for this function are considered and it is shown that all of the alternatives lead to approximately the same predictions. Comparison of theory and experiment indicates that the EG model description of the recent Fermilab data of Donaldson et al is good to approximately 15-20% per data point over a range of more than 105 in the magnitude of the inclusive cross section.