Dean Gibson' s side led after the opening 45 minutes at Petershill Park, defender Siobhan Hunter's superb finish in the 19th minute following Rachael Boyle's free-kick.
But the hosts produced an emphatic response in the second half, Amy Bulloch scoring from the penalty spot seven minutes after the restart and ten minutes later the Jags turned the game on its head when Rebecca McFowan netted. Things went from bad to worse for the Hibees two minutes later as Bulloch got her second and Thistle's third.
The visitors did reduce the arrears as Colette Cavanagh headed in for 3-2 and, despite throwing everything at their opponents in the final stages, they were unable to find an equaliser.
Elsewhere, Spartans Women were forced to settle for a goalless draw against Motherwell at Ainslie Park.
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Debbi McCulloch's players enjoyed the majority of possession, creating the clearer chances but were unable to find the breakthrough.
Meanwhile, Hearts lost out 2-0 to champions Glasgow City at Oriam. City went in front in the tenth minute through Aoife Colvill, the youngster first to react following a good stop by Jambos no.1 Charlotte Parker-Smith.
Grant Scott's side doubled their advantage three minutes before the half-time break through Hayley Lauder's close-range finish.
In SWPL 2, Boroughmuir Thistle were narrowly defeated 2-1 by league leaders Dundee United at Meggetland, the home side assuming the lead through Elvie McLean's penalty.