Inclusive cross sections for both jet and pion production in proton-proton collisions are calculated for the first time fully based on unintegrated gluon, quark and antiquark distributions (uPDF). We use recently developed Kwiecinski uPDF's and different phenomenological fragmentation functions from the literature. In addition to the gg -> g diagram (used recently for applications at RHIC) we include also gq -> q and qg -> q diagrams for inclusive parton production. The cross section for pions is obtained then by convoluting the parton distributions and fragmentation functions. We discuss competition of the different contributions in the whole phase space. We find that the new contributions are comparable to the purely gluonic one at midrapidities and dominate in the fragmentation region (large x_F or large rapidity). The new mechanisms are responsible for pi^+ - \pi^- asymmetry, especially at SPS energies. We discuss how the asymmetry depends on x_F (or rapidity) and p_t.