This Letter reports a measurement of the top quark mass, MtopMtop, in data from pp collisions at √s=1.96 TeV corresponding to 2.7 fb−1 of integrated luminosity at the Fermilab Tevatron using the CDF II detector. Events with the lepton+jets topology are selected. An unbinned likelihood is constructed based on the dependence of the lepton transverse momentum, PTPT, on MtopMtop. A maximum likelihood fit to the data yields a measured mass Mtop=176.9±stat8.0±syst2.7 GeV/c2Mtop=176.9±8.0stat±2.7syst GeV/c2. In this measurement, the contribution by the jet energy scale uncertainty to the systematic error is negligible. The result provides an important consistency test for other MtopMtop measurements where explicit use of the jet energy is made for deriving the top quark mass.