We study single jet and prompt-photon inclusive hadroproduction with multi-Regge kinematics invoking the hypothesis of parton Reggeization in t-channel exchanges at high energy. In this approach, the leading contributions are due to the fusion of two Reggeized gluons into a Yang-Mills gluon and the annihilation of a Reggeized quark-antiquark pair into a photon, respectively. Adopting the Kimber-Martin-Ryskin and Blumlein prescriptions to derive unintegrated gluon and quark distribution functions of the proton from their collinear counterparts, for which we use the Martin-Roberts-Stirling-Thorne set, we evaluate cross section distributions in transverse momentum (p(T)) and rapidity. Without adjusting any free parameters, we find good agreement with measurements by the CDF and D0 Collaborations at the Tevatron and by the ATLAS Collaboration at the LHC in the region 2p(T)/root S less than or similar to 0.1 where root S is the hadronic c.m. energy.