  We present a method for the first principles calculation of tachyon one-point
amplitudes in $(2,2p+1)$ minimal Liouville gravity defined on a torus. The
method is based on the higher equations of motion in the Liouville CFT. These
equations were earlier successfully applied for analytic calculations of the
amplitudes in the spherical topology. We show that this approach allows to
reduce the moduli integrals entering the definition of the torus amplitudes to
certain boundary contributions, which can be calculated explicitly. The results
agree with the calculations performed in the matrix models approach.
