Berwick maintained fourth position in the Third Division despite a shock 2-0 home defeat to Annan.
Rangers' midfielder Steven Notman was the first to threaten the goal but his left-footed shot from six yards out was parried by goalkeeper Alex Mitchell.
Mitchell again proved crucial when he saved a Kevin McDonald header from close range while the home side were dealt a blow when their leading scorer Darren Lavery was replaced due to injury.
Just before the break Annan took the lead when Scott Chaplain showed great technique to volley in from six yards.
In the 87th minute Berwick's Lee Currie was dismissed for a second bookable offence, before Annan doubled their lead with a superb 35-yard strike by Martin McNiff.