The Norwegian, who picked up her first individual win of the season in the 15km pursuit win on Saturday, proved she is a serious contender to defend her individual sprint and pursuit crowns in Sochi next year.
She is now the most successful individual in Davos with five wins, after she pipped Randall to the line by one-hundredth of a second in a time of 2:57.60minutes.
Denise Herrmann of Germany took the bronze while Great Britain's Rosamund Musgrave finished in 51st place with a time of 3:07.00mins.
But it is Bjoergen, with 62 career wins, who continues to impress, leading the overall standings with 569 points, 108 ahead of Charlotte Kalla of Sweden and compatriot Therese Johaug.
And it proved to be a double Norway success as Anders Gloersen raced clear of the field in a time of 2:38.74mins for his first win since Holmenkollen in 2010.
Gloersen was 0.59secs ahead of Martti Jylhae of Finland in second and Sergey Ustiugov of Russia in third, both of whom took their first ever World Cup podiums.
Andrew Young won the battle of the Brits, finishing in 29th, five places above Andrew Musgrave, in a time of 2:38.12mins.
Martin Johnsrud Sundby, who finished 48th in the sprint and third in Saturday's 30km pursuit, continues to lead the overall standings.