An original extrapolation technique developed previously is modified and applied to study nuclear reactions in the ⁶Li + T system at energies E = 0-2 MeV. Cross sections of gamma-ray-producing reactions ⁶Li(t,d₁)⁷Li*[0.478] and ⁶Li(t,p₁)⁸Li*[0.981] with important diagnostic implications are calculated. The (t,d₁) nuclear data found exceed those accepted elsewhere by 2.5-3.5 times at sub-barrier energies. The cross sections of the (t,p₁) reaction are calculated for the first time.