19 pagesOne interpretation of proton stability is the existence of extra-flat directions of the MSSM, in particular u^{c}u^{c}d^{c}e^{c} and QQQL, where the operators lifting the potential are suppressed by a mass scale Λ which is much larger than the Planck mass, Λ >~ 10^{26} GeV. Using D-term hybrid inflation as an example, we show that such flat directions can serve as the inflaton in SUSY inflation models. The resulting model is a minimal version of D-term inflation which requires the smallest number of additional fields. In the case where Q-balls form from the extra-flat direction condensate after inflation, successful Affleck-Dine baryogenesis is possible if the suppression mass scale is >~ 10^{31}-10^{35} GeV. In this case the reheating temperature from Q-ball decay is in the range 3-100 GeV, while observable baryon isocurvature perturbations and non-thermal dark matter are possible. In the case of extra-flat directions with a large t squark component, there no Q-ball formation and reheating is via conventional condensate decay. In this case the reheating temperature is in the range 1-100 TeV, naturally evading thermal gravitino overproduction while allowing sphaleron erasure of any large B-L asymmetry.The work of O.S. is supported by the MEC project FPA 2004-02015 and the Comunidad de Madrid project HEPHACOS (No. P-ESP-00346). The work of JM was supported (in part) by the European Union through the Marie Curie Research and Training Network ”UniverseNet” (MRTN-CT-2006-035863) and by STFC (PPARC) Grant PP/D000394/1.