Weak boson fusion promises to be a copious source of intermediate mass Standard Model Higgs bosons at the LHC. The additional very energetic forward jets in these events provide for powerful background suppression tools. We analyze the H -> W^(*)W^(*) -> e mu pTmiss decay mode for a Higgs boson mass in the 130-200 GeV range. A parton level analysis of the dominant backgrounds (production of W pairs, tt~ and Z -> tau tau in association with jets) demonstrates that this channel allows the observation of H -> W^(*)W^(*) in a virtually background-free environment, yielding a significant Higgs boson signal with an integrated luminosity of 5 fb^-1 or less. Weak boson fusion achieves a much better signal to background ratio than inclusive H -> e mu pTmiss and is therefore the most promising search channel in the 130-200 GeV mass range.