Bjoergen and overall World Cup winner Weng started with a 29-second lead and worked in tandem to stay well in front of the chasing pack.
And in the end Bjoergen crossed the line in 22:36.1 minutes to claim victory, with Weng 1.2 seconds behind.
And completing the podium was Swede Stina Nilsson as she beat team-mate Ida Ingemarsdotter to the third spot.
Krista Parmakoski of Finland finished second in overall standings as she came home fifth, while Ingvild Flugstad Oestberg of Norway was third as she was one place further back.
Read the original article on Eurosport: Bjoergen beats team-mate Weng in World Cup finale