Randall, who won the opening prologue stage, dropped from first overall to 14th after the pursuit but comprehensively took victory in the sprint in Switzerland.
She led the final in Val Mustair from start to finish breaking away from the rest of the field in the latter stages to win a time of 3:37.0minutes.
Norway’s Oestberg took second 8.7seconds behind Randall while Norwegian teammate Heidi Weng finished third a further 1.9 adrift.
Justyna Kowalczyk, who has won the past three Tour de Ski titles and took a dominant victory in the pursuit, failed to make the final but still leads overall.
She tops the standings with an overall time of 35:08.0 with Therese Johaug, who was knocked out of the same semi-final as Kowalczyk, still second with 35:58.3.
Randall’s yo-yoing up and down the overall standings continues as she now sits fifth in 36:26.1 and the American was more than satisfied with her win.
She said: “The crowd out there were great. The course was really tough but really fun and I am happy to have had a great day on my skis.”