The Edinburgh side took the lead through Faye after only seven minutes, but by half-time Rangers were back on level terms with a goal from Sean Stewart.
In the second half, Lewis Barr slotted the ball past the advancing keeper for 2-1 and Scobbie netted a third after 85 minutes to complete the victory.
The win places Berwick seventh in the table on 40 points from their 24 games.
On Saturday (January 22) Rangers are away to Hill of Beath Hawthorn in the East of Scotland Qualifying Cup, kick-off 2.30pm.
In the East of Scotland League, Tweedmouth Rangers were due to travel to take on Ormiston in what would have been their first game in eight weeks.
However, just a few hours before kick-off, their opponents said they were unable to fulfil the fixture and the match was postponed.
Tweedmouth will now be looking to kick-start their season again this Saturday with an away match against Bo’ness in the King Cup second round.
In the Border Amateur League, Tweedmouth Amateurs were without a game.
In the C Division, Highfields played their first match since the festive break and picked up three points with a 2-0 away win over Gala Fairydean Rovers Colts. Goals for the Berwick side came from K Yule and L Dodd.
Berwick Colts lost 2-1 at home to Hawick Colts.
BAL fixtures for Saturday are:
B League - Tweedmouth Ams v Biggar.
C League - Berwick Colts v Eyemouth United; Highfields United v Spittal Rovers.
In the Northern Alliance League, North Sunderland won 4-1 away to Blyth Town U23s in Division 3 with two goals from Chris Gardner and one each from Kevin Elliott and Liam Cravagan.
The win puts the Seahouses side seventh in the table with 23 points from 13 games. This weekend they are home to Bedlington United Sporting Club.
In the North Northumberland League, Berwick Town recorded their first ever victory with a 3-2 home win over Longhoughton Rangers at Lowick, whilst Wooler went down 6-1 at home to Alnmouth.