The process e+e-→ K+K-π is studied with the SND detector at the VEPP-2000 e+e- collider. Basing on data with an integrated luminosity of 26.4 pb - 1 we measure the e+e-→ K+K-π cross section in the center-of-mass energy range from 1.28 up to 2 GeV. The measured mass spectrum of the Kπ system indicates that the dominant mechanism of this reaction is the transition through the K∗(892) K intermediate state. The cross section for the ϕπ intermediate state is measured separately. The SND results are consistent with previous measurements in the BABAR experiment and have comparable accuracy. We study the effect of the interference between the ϕπ and K∗K amplitudes. It is found that the interference gives sizable contribution to the measured e+e-→ ϕπ→ K+K-π cross section below 1.7 GeV.