We report measurements of charmless hadronic B0 decays into the π+π-K+π- final state. The analysis uses a sample of 657×106 BB̄ pairs collected with the Belle detector at the KEKB asymmetric-energy e+e- collider at the resonance. The decay B0→ρ0K+π- is observed for the first time; the significance is 5.0σ and the corresponding partial branching fraction for MKπ(0.75,1.20)GeV/c2 is [2.8±0.5(stat) ±0.5(syst)]×10-6. We also obtain the first evidence for B0→f0(980)K+π- with 3.5σ significance and for B0→π+π- K0 with 4.5σ significance. For the two-body decays B0→ρ0K0 and B0→f0(980)K*0, the significances are 2.7σ and 2.5σ, respectively, and the upper limits on the branching fractions are 3.4×10-6 and 2.2×10-6 at 90% confidence level. © 2009 The American Physical Society.