Product recoils from the reaction $^{96}\mathrm{Ru}$ +255 MeV $^{58}\mathrm{Ni}$ \ensuremath{\rightarrow} $^{154}\mathrm{Hf}^{\mathrm{*}}$ were analyzed using the Argonne Fragment Mass Analyzer and transported to a collector foil behind the focal plane, where decay of \ensuremath{\mu}s isomers could be studied under low background conditions. The recoils were dispersed in A/q as they traversed the position-sensitive focal-plane detector, and recoil--\ensuremath{\gamma}-ray coincidences could thus be used to assign masses for specific \ensuremath{\gamma}-ray cascades. By use of these methods, yrast isomers with half-lives of 2.6(7) \ensuremath{\mu}s and 20(1) \ensuremath{\mu}s have been firmly assigned to the exotic N=81 nucleus $^{151}\mathrm{Yb}$, and the main features of the isomeric decays have been established. The yrast level structure of $^{151}\mathrm{Yb}$ and lighter N=81 isotones are compared.