East Fife enhanced their play-off hopes, and killed off Berwick’s entirely, when they won a key game at Shielfield on Saturday.
The victory leaves the Fifers three points ahead of Annan in the race for fourth with just one game to go.
Berwick, who had Lee Currie sent off in the second half, were left to lick their wounds.
Kevin Smith netted twice for the visitors with Jonathan Page bagging the other.
This was a must win game for Berwick, who knew that any result other than a victory would signal the end of their play-off hopes.
Just two minutes in Michael Andrews made a good reaction save to turn a shot from Ross Brown.
At the other end Blair Henderson almost got in, bit under pressure from a defender he was unable to get his shot away.
Henderson also fired wide after half an hour’s play, but in truth this was a game of few chances.
The breakthrough came after 35 minutes when Kevin Smith turned and fired low into the bottom corner past Andrews after taking a cross pass from Fraser Mullen.
Rangers tried to force their way back into the game before half-time but Kyle Wilkie and David Gold were both off target and Fifers’ keeper Alan Fleming remained untroubled.
In the second half Berwick again pressed for an equaliser without being threatening, but they were almost caught out after 54 minutes when Allan Walker burst through the middle, but his shot was tipped around the post for a corner by Andrews at full stretch.
Stephen Tulloch had a header from a Lee Currie corner headed off the line and second later Nathan Austin went close at the other end for the visitors as play started to open up.
Berwick were then reduced to ten men after 63 minutes when Lee Currie was shown a straight red card by referee Steven Kirkland for a needless foul from behind on Fifers’ full back Scott Smith close to the half-way line..
Rangers immediately introduced striker Darren Lavery at the expense of full back Devon Jacobs to try and force the issue, but after 71 minutes East Fife doubled their advantage when Jonathan Page stooped and headed in a rebound from close range after Andrews clawed a shot off the line at full stretch.
Scott Maxwell fired in a shot from outside the box which Fleming tipped over for a corner and from the set piece Jonny Fairbairn headed over the bar.
East Fife rammed home their superiority after 83 minutes when Kevin Smith shot low into the bottom corner for his second of the afternoon, putting his side in the box seat going into the final game of the season.
A point from their final game against Elgin will be enough to see them through.
Berwick, meanwhile, must try and regroup for their final game of the season away to Arbroath this weekend.