We derive the two-loop QCD helicity amplitudes for the processes ℓq→ℓqg (View the MathML source) and View the MathML source, which are the partonic reactions yielding (2+1)-jet final states in deep inelastic lepton nucleon scattering. The amplitudes are obtained by analytic continuation of the known helicity amplitudes for View the MathML source. We separate the infrared divergent and finite parts of the amplitudes using Catani's infrared factorization formula. The analytic results for the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic polylogarithms. To evaluate these functions numerically, we list in detail the non-trivial (and kinematic region dependent) variable transformations one needs to perform.