We present the first measurements of the absolute branching fractions of Ξc+ decays into Ξ-π+π+ and pK-π+ final states. Our analysis is based on a data set of (772±11)×106 BB̄ pairs collected at the (4S) resonance with the Belle detector at the KEKB e+e- collider. We measure the absolute branching fraction of B̄0→Λ̄c-Ξc+ with the Ξc+ recoiling against Λ̄c- in B̄0 decays resulting in B(B̄0→Λ̄c-Ξc+)=[1.16±0.42(stat.)±0.15(syst.)]×10-3. We then measure the product branching fractions B(B̄0→Λ̄c-Ξc+)B(Ξc+→Ξ-π+π+) and B(B̄0→Λ̄c-Ξc+)B(Ξc+→pK-π+). Dividing these product branching fractions by B̄0→Λ̄c-Ξc+ yields B(Ξc+→Ξ-π+π+)=[2.86±1.21(stat.)±0.38(syst.)]% and B(Ξc+→pK-π+)=[0.45±0.21(stat.)±0.07(syst.)]%. Our result for B(Ξc+→Ξ-π+π+) can be combined with Ξc+ branching fractions measured relative to Ξc+→Ξ-π+π+ to set the absolute scale for many Ξc+ branching fractions.