We present the first measurement of the mass of the top quark in a sample of tt→ℓνbbqq events (where ℓ=e,μ) selected by identifying jets containing a muon candidate from the semileptonic decay of heavy-flavor hadrons (soft muon b tagging). The pp collision data used correspond to an integrated luminosity of 2  fb−1 and were collected by the CDF II detector at the Fermilab Tevatron Collider. The measurement is based on a novel technique exploiting the invariant mass of a subset of the decay particles, specifically the lepton from the W boson of the t→Wb decay and the muon from a semileptonic b decay. We fit template histograms, derived from simulation of tt events and a modeling of the background, to the mass distribution observed in the data and measure a top quark mass of 180.5±12.0(stat)±3.6(syst)  GeV/c2, consistent with the current world average value.