Observations of hot Jupiters around solar-type stars with very short orbital periods (∼1 d) suggest that tidal dissipation in such stars is not too efficient so that these planets can survive against rapid orbital decay. This is consistent with recent theoretical works, which indicate that the tidal quality factor, Q★, of planet-hosting stars can indeed be much larger than the values inferred from the circularization of stellar binaries. On the other hand, recent measurements of Rossiter–McLaughlin effects in transiting hot Jupiter systems not only reveal that many such systems have misaligned stellar spin with respect to the orbital angular momentum axis, but also show that systems with cooler host stars tend to have aligned spin and orbital axes. Winn et al. suggested that this obliquity–temperature correlation may be explained by efficient damping of stellar obliquity due to tidal dissipation in the convection zone of the star. This explanation, however, is in apparent contradiction with the survival of these short-period hot Jupiters. We show that in the solar-type parent stars of close-in exoplanetary systems, the effective tidal Q★ governing the damping of stellar obliquity can be much smaller than that governing orbital decay. This is because, for misaligned systems, the tidal potential contains a Fourier component with frequency equal to the stellar spin frequency (in the rotating frame of the star) and rotating opposite to the stellar spin. This component can excite inertial waves in the convective envelope of the star, and the dissipation of inertial waves then leads to a spin–orbit alignment torque and a spin-down torque, but not orbital decay. By contrast, for aligned systems, such inertial wave excitation is forbidden since the tidal forcing frequency is much larger than the stellar spin frequency. We derive a general effective tidal evolution theory for misaligned binaries, taking account of different tidal responses and dissipation rates for different tidal forcing components.