In this paper, we carry out the complete Oðαα 2 s Þ-order study on the inclusive productions of ϒðnSÞ and χ b ðnPÞ (n ¼ 1, 2, 3) via the Standard Model Higgs boson decay, within the framework of nonrelativistic QCD. The feeddown effects via the higher excited states are found to be substantial. The color-octet 3 S ½8 1 state related processes consisting of H 0 → bb½ 3 S ½8 1 þ g and H 0 → bb½ 3 S ½8 1 þ Q þQ (Q ¼ c, b) play a vital role in the predictions on the decay widths. Moreover, our newly calculated next-to-leading order QCD corrections to H 0 → bb½ 3 S ½8 1 þ g can enhance its leadingorder result by 3-4 times, subsequently magnifying the total 3 S ½8 1 contributions by about 40%. Such a remarkable enhancement will to a large extent influence the phenomenological conclusions. For the color-singlet 3 P ½1 J state, in addition to H 0 → bb½ 3 P ½1 J þ b þb, the newly introduced light hadrons associated process, H 0 → bb½ 3 P ½1 J þ g þ g, can also provide non-negligible contributions, especially for 3 P ½1 2. Summing up all the contributions, we have B H 0 →χ b ðnPÞþX ∼ 10 −6-10 −5 and B H 0 →ϒðnSÞþX ∼ 10 −5-10 −4 , which meets marginally nowadays LHC experimental data and can help in understanding the heavy quarkonium production mechanism as well as the Yukawa couplings.