Johaug won in 25 minutes, 23.4 seconds, beating Bjoergen by 10.2. Yulia Tchekaleva of Russia was third, 32.7 seconds behind Johaug.
Bjoergen led at the halfway mark but barely ahead of Johaug, who steadily increased her pace and built a 4.5-second lead after 6.8 kilometers.
Johaug's lead was more than 11 seconds at one point as she skied with teammate Kristin Stoermer Steira.
She won her third world title and her second individual after the 30K in Oslo. Johaug finished second to Bjoergen in the sprint last week.
"For me it is a big day," Johaug said. "I never thought I would do it because Marit is the queen of cross country. When I woke up this morning I had a good feeling. I was really focused and I knew that if I stayed that way I could be on top of the podium.
"All the time I kept hearing I was two seconds behind then one second. I knew if I pushed myself I could do it. I got a lot of help from Kristin at the end of the race, she pushed me all the way and then I heard that I had nine seconds ahead of Marit and I knew I could do it."
Bjoergen, who won the individual sprint and the 15-kilometer pursuit skiathlon, was looking for her 11th world title. The silver is her 17th worlds medal.
"I knew Therese was going to be my hardest rival," Bjoergen said. "I'm very happy for Therese, I train with her. I can see that she is pushing herself very hard to be at her top level and that motivates me too to push myself even more.
"I didn't know until the end of the race. I heard there was about two seconds between us at one point, then she started fighting even harder. I did my best but she was really strong in the last two kilometers."
Miriam Goessner of Germany just missed out on the podium by 0.5 seconds.