We present the first measurements of absolute branching fractions of Ξc0 decays into Ξ−π+, ΛK−π+, and pK−K−π+ final states. The measurements are made using a dataset comprising (772±11)×106 BB¯ pairs collected at the ϒ(4S) resonance with the Belle detector at the KEKB e+e− collider. We first measure the absolute branching fraction for B−→Λ¯c−Ξc0 using a missing-mass technique; the result is B(B−→Λ¯c−Ξc0)=(9.51±2.10±0.88)×10−4. We subsequently measure the product branching fractions B(B−→Λ¯c−Ξc0)B(Ξc0→Ξ−π+), B(B−→Λ¯c−Ξc0)B(Ξc0→ΛK−π+), and B(B−→Λ¯c−Ξc0)B(Ξc0→pK−K−π+) with improved precision. Dividing these product branching fractions by the result for B−→Λ¯c−Ξc0 yields the following branching fractions: B(Ξc0→Ξ−π+)=(1.80±0.50±0.14)%, B(Ξc0→ΛK−π+)=(1.17±0.37±0.09)%, and B(Ξc0→pK−K−π+)=(0.58±0.23±0.05)%. For the above branching fractions, the first uncertainties are statistical and the second are systematic. Our result for B(Ξc0→Ξ−π+) can be combined with Ξc0 branching fractions measured relative to Ξc0→Ξ−π+ to yield other absolute Ξc0 branching fractions.