All the goals were scored in the second half, with the capital side establishing. 2-0 lead through Henderson (50 minutes) and Russel (62) before Lewis Baker pulled a goal back for Rangers after 79.
The loss leaves Berwick eighth in the Lowland League table with 19 points from their 13 games.
On Saturday (October 2), they potentially face what could be one of their hardest home league games of the season when they take on Rangers B at Shielfield.
In the East of Scotland League, Tweedmouth Rangers recorded a good 4-1 home win over Thornton Hibs in the A Conference.
The Berwick side opened the scoring three minutes before half time through Declan Knox.
In the second half, Joe Kinnonmonth equalised for Hibs but Tweedmouth raised their game and goals from Knox, Sean Campbell and Drew Cummings secured the victory, only their second league win of the season, which lifts them to 12th in the table with six points from their nine games.
On Saturday, Tweedmouth are away to Dalkeith Thistle, in a game which kicks off early at 11.15am.
In the Border Amateur League, two Berwick sides both progressed through to cup finals.
In the Wright Cup, Tweedmouth Amateurs maintained their 100 per cent start to the season with a 4-2 win over Gala Hotspur in the semi-finals, their goals coming from Leah, Hope and Antcliffe, who have now netted 21 goals between them so far this season.
Tweedmouth will now face Leithen Rovers in the final.
In the Collie Cup semi-finals, Spittal Rovers, in their first season in the league, beat Eyemouth Amateurs 5-1 away to reach the final. Their goals came from Bloomfield (2), Fairbairn (2) and Jeffrey and they will now go on to meet Hawick Colts in the final.
Berwick Colts won 2-1 at home against Gala Fairydean Rovers in the C League.
BAL fixtures for Saturday are: B League - Earlston Rhymers v Tweedmouth Ams; C League - Cavalry Park v Spittal Rovers; Gala FR v Berwick Colts; Highfields v Eyemouth Ams.