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 BB̄ pairs collected at the (4S) resonance with the Belle detector at the KEKB e+e-collider. We first measure the absolute branching fraction for B-→Λ̄c-Ξc0 using a missing-mass technique; the result is B(B-→Λ̄c-Ξc0)=(9.51±2.10±0.88)×10-4. We subsequently measure the product branching fractions B(B-→Λ̄c-Ξc0)B(Ξc0→Ξ-π+), B(B-→Λ̄c-Ξc0)B(Ξc0→ΛK-π+), and B(B-→Λ̄c-Ξc0)B(Ξc0→pK-K-π+) with improved precision. Dividing these product branching fractions by the result for B-→Λ̄c-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.