We present the first model-independent measurement of the absolute branching fraction of the Λc+→pK-π+ decay using a data sample of 978fb-1 collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. The number of Λc+ baryons is determined by reconstructing the recoiling D(*)-p̄π+ system in events of the type e+e-→D(*)-p̄π+Λc+. The branching fraction is measured to be B(Λc+→pK-π+)=(6.84±0.24-0.27+0.21)%, where the first and second uncertainties are statistical and systematic, respectively. © 2014 American Physical Society.