Hibs had the better start and Tegan Bowie almost made it 1-0 when she got ahead of the Rangers defence but her low effort was kept out by Vic Esson.
Kathleen McGovern opened the scoring minutes later when she chipped over the Rangers goalkeeper.
The striker found a second with just over 10 minutes to play when she capitalised on a slip up from the Rangers defence and smashed the ball into the top corner.
Substitute Rosie Livingstone made it three when she fired beyond Esson into the inside netting.
The result moves Hibs to within two points of Edinburgh rivals Hearts, and three behind Rangers who slip five behind Glasgow City at the top of the table.
