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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 BB¯ pairs collected at the ϒ(4S) resonance with the Belle detector at the KEKB e+e− collider. We measure the absolute branching fraction of B¯0→Λ¯c−Ξc+ with the Ξc+ recoiling against Λ¯c− in B¯0 decays resulting in B(B¯0→Λ¯c−Ξc+)=[1.16±0.42(stat.)±0.15(syst.)]×10−3. We then measure the product branching fractions B(B¯0→Λ¯c−Ξc+)B(Ξc+→Ξ−π+π+) and B(B¯0→Λ¯c−Ξc+)B(Ξc+→pK−π+). Dividing these product branching fractions by B¯0→Λ¯c−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.