Tweedmouth were looking to avenge their 2-1 defeat away at Thornton Hibs when they faced them on Saturday, but went in at the interval 1-0 down.
The Hibs goal came from a 39th minute penalty after Tweedmouth skipper Regan Graham was adjudged to have pushed over Stuart Drummond in the area.
Drummond had twice failed to find the target from free kicks, but he made no mistake with his spot kick, putting it past Niall Frampton to give Hibs the edge in an even first half.
Graham had a couple of efforts on goal himself in the first half, testing the Hibs keeper, Calum Sutherland.
Sutherland was also called into action from a Graham free kick, punching the ball away.
Graham got his goal six minutes after the restart when pressure by Jack Cummings resulted in Sutherland scuffing an attempted clearance.
The ball fell to Kyle Wood, he passed to Graham and he found the net as Sutherland tried to get back between the posts.
Hibs twice came close to taking the lead, Dean Mcmillan shooting over the bar and then seeing his cross pushed away by Frampton.
Frampton was called into action again, saving a shot by Andrew Adam, and Hibs saw a header hit the bar as they continued to attack.
Rangers held firm thanks to some great defending by the back three of Craig Heath, Kieran Cromarty and Jordan Crombie, and Rhys Dixon endeavoured to keep Tweedmouth going forward with some searching passes.
Dixon was instrumental in Tweedmouth’s 85th minute winner, passing the ball to Graham.
He moved the ball on to Jack Forster, who found himself in loads of space and played the ball forward to Graham.
The captain made no mistake, grabbing the winner with one of the best goals scored by Tweedmouth this season.
Tweedmouth play Lochgelly Albert at Old Shielfield on Saturday (May 20) for their last home game of the season before travelling to Newburgh Juniors at East Shore Park on Saturday, May 27, for their last game of the season.