We explore for the first time the possibilities to measure an intermediate-mass (m H = 115 -140 GeV/c 2 ) Standard-Model Higgs boson in electromagnetic proton-lead (p Pb) interactions at the CERN Large Hadron Collider (LHC) via its bb decay. Using equivalent Weizsäcker-Williams photon fluxes and Higgs effective field theory for the coupling γ γ → H, we obtain a leading-order cross section of the order of 0.3 pb for exclusive Higgs production in elastic (p Pb γ γ − − → p H Pb) and semielastic (p Pb γ γ − − → X H Pb) processes at √ s NN = 8.8 TeV. After applying various kinematics cuts to remove the main backgrounds (γ γ → bb and misidentified γ γ → qq events), we find that a Higgs boson with m H = 120 GeV/c 2 could be observed in the bb channel with a 3σ-significance integrating 300 pb −1 with an upgraded p A luminosity of 10 31 cm −2 s −1 . We also provide for the first time semielastic Higgs cross sections, along with elastic tt cross sections, for electromagnetic pp, p A and AA collisions at the LHC .