The Russians dominated for the second day in a row to build on their overnight lead and retain the crown they won in Bergen, Norway in 2010.
Germany came second and Ukraine third ahead of Britain with one event to go.
Tatanya Dektyareva won the 100 meters hurdles and Darya Klishina the long jump to lay the foundations for Russia early in the second day, Klishina jumping just one centimeter more than local favorite Kluft.
The former world, European and Olympic heptathlon champion has been plagued by injuries and poor form in recent years, but recorded a jump of 6.73 with her first attempt, her best for three years.
It also took Kluft over the world championship qualification mark of 6.65, meaning she can compete at this year's event in Daegu, South Korea.
French sprinter Christophe Lemaitre set his second championship record in two days, winning the men's 200 meters in a time of 20.28.
"It's only my second 200 of the season, so I'm happy with the time," he told Sweden's SVT.
Lemaitre's was one of the few fast times on the sodden track as the second day was beset by heavy rain and unseasonably cold temperatures, with the organizers forced to move the men's pole vault to an indoor venue.
With 39 of the 40 events completed, Russia had an unassailable lead with 375 points ahead of Germany, Ukraine and Britain.
