We analyze the production and subsequent decay of the neutral Higgs bosons h ≡ h 0 , H 0 , A 0 of the MSSM into electrically neutral quark pairs of different flavors (qq ′ ≡ tc, bs, depending on h) at the LHC, i.e. σ(pp → h → qq ′ ), and compare with the direct FCNC production mechanisms σ(pp → qq ′ ). The cross-sections are computed in the unconstrained MSSM with minimal flavor-mixing sources and taking into account the stringent bounds from b → sγ. We extend the results previously found for these FCNC processes, which are singularly uncommon in the SM. Specifically, we report here on the SUSY-EW part of σ(pp → h → qq ′ ) and the SUSY-QCD and SUSY-EW contributions to σ(pp → bs). In this way, the complete map of MSSM predictions for the qq ′ -pairs produced at the LHC becomes available. The upshot is that the most favorable channels are: 1) the Higgs boson FCNC decays into bs, and 2) the direct production of tc pairs, both of them at the ∼ 1pb level and mediated by SUSY-QCD effects. If, however, the SUSY-QCD part is suppressed, we find a small SUSY-EW yield for σ(pp → h → tc) max ∼ 10 −4 pb but, at the same time, σ(pp → h → bs) max ∼ 0.1 − 1 pb, which implies a significant number (∼ 10 4 − 10 5 ) of bs pairs per 100 fb -1 of integrated luminosity.