Click here to watch the full highlights on Recast.
After a victory away to Aberdeen on Sunday in the SWPL Cup quarter final, the Hibees travelled to New Douglas Park.
Dean Gibson made one change from that game with Emily Mutch coming in for Gabby English.
The away side controlled the majority of possession in the opening exchanges, with Shannon Leishman and Toni Malone causing Accies problems down the right hand side.
However, clear cut chances were at a premium due to resolute defending and wasteful play on Hibs' behalf.
Our hosts for the evening would create the first real opportunity of the game with Josi Giard breaking through the defence and finding herself one-on-one with Mutch. The 'keeper forced Giard into an early shot which fired into the side netting.
As the Hibees settled into the game, the attacking play became more fluid, eventually leading to the first and decisive goal just before the half hour mark.
Amy Muir and Rachael Boyle linked up on the left side of the Accies box before the former floated in a lovely ball to Gallacher who tapped in beyond Jeni Currie.
The referee drew the first half to a close with the Hibees taking in the lead.
As the two sides emerged for the second period, Gibson made a half time substitution with Alexa Coyle coming on for Malone.
The American striker caused Hamilton problems from the get go with her driving runs in behind.
The second half followed much of the same pattern as the first with Hibs dominating possession, although a few more chances were created.
The first fell to another second half substitute, Leah Eddie, who received the ball on the edge of the box and almost had the travelling fans off their seats but her low effort went inches wide of the post.
Hibs continued to push for a second and a bit of breathing space going into the final stages but just couldn't find that vital opening.
One goal proved to be enough, however, with Gibson's side picking up another hard fought but deserving win away from home.
Line up: Mutch, Leishman (Eddie, 70'), Muir, Hunter, Malone (Coyle, 46'), McGregor (Morrison, 60'), Cavanagh, Gallacher, Notley, Murray (C), Boyle
Unused subs: English, Adams
