Rangers lost 2-1, their opponents doing just enough to pip the Shielfielders for sixth place in the final league table.
Offord gave the home side a 1-0 half-time lead, but after the break Sean Stewart equalised for Berwick in the 75th minute.
East Stirlingshire snatched all three points with a second goal from Offord in the 89tb minute.
Rangers finished the season in eighth with 54 points from their 34 games.
Next Saturday (April 23), Berwick will contest the knock-out stages of the Lowland League Cup.
After coming through the qualifying groups, Stuart Malcolm’s side are away to East Kilbride in the quarter-finals.
Other ties are: Gala Fairydean Rovers v Broomhill; East Stirlingshire v Caledonian Braves; and Edinburgh University v Bo’ness United.
In the East of Scotland League, Tweedmouth Rangers were away to Edinburgh United in the A Conference where they lost 1-0, leaving them 13th in the table.
On Saturday they are away from home again when they travel to take on fifth in the table Rosyth.
In the Border Amateur, Tweedmouth Amateurs recovered from their first loss of the season against B League rivals Stow to beat Coldstream 3-1 away from home in midweek.
Goalscorers were Michael Antcliffe (2) and Charlie Warcup, but the game had to be abandoned after 67 minutes due to an injury sustained by one of the Coldstream players. It was later confirmed the result will stand.
The win puts Tweedmouth five points clear at the top of the table with four games to play.
In the C Division, Spittal Rovers won 4-0 at home in midweek against Eyemouth Amateurs. On Saturday they faced Langlee Amateurs in the semi-final of the Waddell Cup at home. Unfortunately, they went down to a 2-1 defeat, Hargreaves scoring a late goal for Spittal after earlier strikes from Simpson and Sutherland.
Highfields United lost 3-2 at home to St Boswells in the C Division.
BAL fixtures for Saturday are:
B Div - Tweedmouth Ams v Gala Hotspur. C Div - Lauder v Berwick Colts; Tweeddale Colts v Spittal Rovers.