Heading to the event in Russia Takanashi of Japan had been unstoppable having topped the podium in the first four events of the season.
But Avvakumova made the most of home advantage as she scored 249.2 points for victory.
And Takanashi had to settle for bronze in Chaikovsky as German Carina Vogt picked up her second successive silver medal.
Despite not topping the podium for the first time this season Takanashi is still leading the overall World Cup standings on 460 points.
Although for the first time her lead has been cut with Avvakumova second on 315 and Vogt third on 306.