We report on the first observation of D10(2420)→D0π-π+ and D1+(2420)→D+π-π+ decays (where the contribution from the dominant known D1→D*π decay mode is excluded) in the B-→D10π- and B̄0→D1+π- decays, respectively. The observation is based on 15.2×107 BB̄ events collected with the Belle detector at the KEKB collider. We also set 90% confidence level upper limits for the branching fractions of the four following decays: B-→D10π-, D10→D *0π-π+, B̄0→D1+π-, D1+→D*+π-π+, B-→D2*0(2460)π-, D2*0→D*0π-π+, B̄0→D2*+(2460)π-, D2*+→D*+π-π+. © 2005 The American Physical Society.