Charlie Wellings’ 91st-minute goal earned Celtic the win that continued their unbeaten start to the domestic season and knocked Hibernian off the top of the SWPL.
Sarah Harkes had given Fran Alonso’s side a 67th-minute lead at the Penny Cars Stadium in Airdrie.
Collete Cavanagh thought she had secured at least a point for Hibs with a long-range shot 12 minutes from time.
But Wellings found the top corner in time added on.
Elsewhere, Aberdeen are level on points with the new league leaders Celtic after they drew 0-0 with Spartans.
Hearts host Rangers, and champions Glasgow City travel to Hamilton later on Sunday.