For the fourth successive match Berwick kept a clean sheet. All their experienced strikers were superb and Kevin McLeish was outstanding as a stand-in full-back.
But in the first half the youngsters carried a real sting. Visiting goalkeeper Willie McCoullogh had a find a double save from Sean Paliszka and Gareth Hutchinson, and then another from Danny Swanson.
Stenhousemuir were always dangerous and Paul McGrillen hit the crossbar.
In the early stages of the second half, the game swung from end to end but the visitors turned up the heat and battered the home defence.
Rangers manager John Coughlan was forced to bring on three youngsters from his under-19's and they played their part in holding on for victory.
Gary O'Connor made a matchwinning stop from Iain Diack and John Paul McBride was inches away with two well-struck free-kicks.
Jim Mercer and Diack also came close, but Berwick almost snatched a winner when Mark Ramsey just failed to reach a Stephen Manson cross which flashed across the goalmouth.