Alan Gow, being tracked by English and Scottish clubs, gave the Bairns an early boost with a beautifully struck goal after nine minutes. His 25-yarder sped into the top corner.
He followed up by heading a Liam Craig cross against the crossbar then forced young Berwick goalkeeper Chris Flockhart into three great saves.
Rangers worked hard but rarely looked dangerous until just after the restart when Kevin Haynes beat two defenders inside the box but shot straight at Jeroen Lambers.
After 51 minutes slick Falkirk went two-up Kenny Milne's cross was flicked on through the box and Craig volleyed home.
Steven Noble missed a great chance immediately afterwards when he shot over after Robbie Manson broke clear.
In an exciting closing quarter Flockhart saved well again from Gow and substitute John Stewart, while Ryan McCallum twice went close for a Rangers side which kept running strongly to the end.
They were unable to break down an excellent defence which was solid and well organised throughout.