Brian O'Driscoll, who usually skippers the side, and fellow centre Gordon D'Arcy, blindside flanker Stephen Ferris and experienced lock Paul O'Connell have all been given Sunday off as Kidney made 10 changes the team that stunned the Wallabies.
"I think in tournament rugby it's extremely difficult to play in games non-stop," Kidney said.
"These guys who are playing here have been training very well, and I think they're the best men to represent us in this match."
Jonathan Sexton drops to the bench to allow Ronan O'Gara to start at fly-half, while Keith Earls moves in from the wing to partner Paddy Wallace, who will also make his World Cup debut, in the centres.
"I always say to the lads, the easiest job here is playing one to 15. The difficult job is not being in the starting 15," Kidney added.
"What Paddy has contributed would be an example for every young player coming through of how to give to the squad without always wanting yourself.
"He's been as disappointed as any man I've ever left off, but he always takes some time for himself then comes back and feeds it back into the team."
Cullen replaces O'Connell in the second row, while Donnacha Ryan will play at blindside flanker, joining the back row duo of number eight Jamie Heaslip and openside Sean O'Brien who impressed so much against Australia.
The front row was also overhauled with loosehead prop Cian Healey, the only survivor of last Saturday's match at Eden Park, joined by hooker Sean Cronin and tighthead Tony Buckley.
The Irish, who won their opening Pool C match against the United States, will be strong favourites to beat the Russians, who have lost their first two matches.
Kidney said the changes did not mean they were taking victory, nor a bonus point for scoring four tries or more, for granted against the World Cup debutants.
"We have a saying back home, we're going to try to get the four bonus points," he added. "Let's see if we can get a win first, and if we can win the match then we'd be delighted with the four."
Ireland: 15-Rob Kearney, 14-Fergus McFadden, 13-Keith Earls, 12-Paddy Wallace, 11-Andrew Trimble, 10-Ronan O'Gara, 9-Isaac Boss, 8-Jamie Heaslip, 7-Sean O'Brien, 6-Donnacha Ryan, 5-Leo Cullen (captain), 4-Donncha O'Callaghan, 3-Tony Buckley, 2-Sean Cronin, 1-Cian Healy.
Russia: 15-Vasily Artemyev, 14-Denis Simplikevich, 13-Andrey Kuzin, 12-Sergey Trishin, 11-Vladimir Ostroushko, 10-Konstantin Rachkov, 9-Alexander Yanyushkin (captain), 8-Victor Gresev, 7-Andrey Garbuzov, 6-Artem Fatakhov, 5-Adam Byrnes, 4-Denis Antonov, 3-Alexander Khrokin, 2-Valery Tsnobiladze, 1-Sergey Popov.
Replacements: 16-Evgeny Matveev, 17-Ivan Prishchepenko, 18-Alexey Travkin, 19-Alexander Voytov, 20-Andrey Bykanov, 21-Mikhail Sidorov, 22-Mikhail Babaev.