Power utility Eskom on Wednesday called on consumers to switch off geysers, pool pumps and all non-e.
The three-day tournament won by New Zealand in both men and women's competitions was staged at the Luzhniki Stadium, the venue for the 1980 Olympic Games that has a capacity of 79000, reduced to 50000 by advertising hoardings.
But the high-octane action of the abbreviated game on the pitch has often been watched by sparsely filled stands.
Brett Gosper, chief executive officer of the International Rugby Board, said that searing temperatures, a massive thunderstorm on the final day and issues with tickets were to blame for some people staying away, but they still claimed daily attendances of around 20000.
"We came to Moscow to take the game to another part of the world, where the sport is developing strongly but is still in its infancy," Gosper said. "We're probably a touch disappointed. We would have liked to have seen a few more people in the crowd, but we've been pushing 20000 a day for this stadium.
"We could have made a choice and put this in a smaller stadium and burst the seams of a 20000-seat stadium, but in Russia doing it in this stadium sends out an enormous signal to the Russians that this is a sport that is really top level. It has an iconic value in that representation."
The Russian men sent the crowds wild with victory in the final of the men's bowl, the third-tier competition, running out convincing 29-5 winners over Japan.
They had beaten Spain 17-7 and Uruguay 38-0 to get there, having gone down to South Africa (31-0) and Scotland (21-5), and drawing with Japan (12-12) in pool play.
The Russian women also pulled off what was arguably the biggest shock of the tournament, edging England 17-15 in pool play. But they could not continue their fine pool-topping form and were eliminated by Canada in the Cup quarters.