Measurements of K^∗(892) resonance production via its K⁺π^- decay mode in inelastic p+p collisions at beam momenta 40 and 80 GeV/c (sNN=8.8 and 12.3 GeV) are presented. The data were recorded by the NA61/SHINE hadron spectrometer at the CERN Super Proton Synchrotron. The template method was used to extract the K^∗(892) signal. Transverse momentum and rapidity spectra were obtained. The mean multiplicities of K^∗(892) mesons were found to be (35.1 ± 1.3 (stat) ± 3.6 (sys)) · 10 ^{- 3} at 40 GeV/c and (58.3 ± 1.9 (stat) ± 4.9 (sys)) · 10 ^{- 3} at 80 GeV/c. The NA61/SHINE results are compared with the Epos1.99 and Hadron Resonance Gas models as well as with world data. The transverse mass spectra of K^∗(892) mesons and other particles previously reported by NA61/SHINE were fitted within the Blast-Wave model. The transverse flow velocities are close to 0.1–0.2 of the speed of light and are significantly smaller than the ones determined in heavy nucleus-nucleus interactions at the same beam momenta.