The Norwegian began the day with a 32.6 second lead over her teammate Heidi Weng after victory on stage two on Sunday, which was also in Lenzerheide.
And she was able to extend that by a further two tenths of a second after picking up bonus seconds at the finish line for the win, leaving her well placed going into the first rest day of the Tour.
Tour de Ski
Oestberg leads the way at Tour de Ski
31/12/2017 AT 19:00
Austria's Teresa Stadlober recorded the fastest time of the day, clear of Russia's Anastasia Sedova and Weng.
But it was Oestberg who took the stage win ahead of Weng with the USA's Jessica Diggins continuing her strong Tour de Ski by taking her first podium finish of the season to hold on to third spot in the overall standings.
Oestberg said: "It was like hell today, it was very hard fight. I felt the snow was not fast. I was gaining seconds on Heidi and then losing them again. It's great to have the red bib for another day but I think I will lose it soon."
Diggins added: "I felt good and strong. I had not bad luck today. I had really good skis too. I was able to ski my own race."
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