First-choice prop Fabien Barcella and Imanol Harinordoquy, among the best flankers in the world, were also left on the bench.
Parra has played little more than 30 minutes at first five-eighths in his career and last played in that position at club level three years ago.
Lievremont, a former international flanker, said he made the decision partly to issue a challenge to his regular first five-eighths, Francois Trinh-Duc, to raise his game after two poor matches.
He had no other option in that position, because Skrela's replacement, the uncapped Jean-Marc Doussain, only arrived on Tuesday from France and will be in no shape to play.
Frederic Michalak, a shorter plane journey away in South Africa, was overlooked despite having more than 50 caps and nine years of international experience playing first five-eighths.
Should France lose, they would be likely to stay in second spot, avoid South Africa and Australia in the knockout stages, and face familiar Northern Hemisphere foes England and Ireland.
Lievremont, who stands down after the tournament, insists his team will go all out for victory at Eden Park.
"It wouldn't be [in the spirit of] rugby to tell the players to give up on a game," he said. "We know that beating New Zealand is always an achievement, and if we do that it will be one. We will do everything to beat New Zealand."
Lievremont, who has tense relations with the French media, could not resist a big dollop of sarcasm when he said: "I will speak to the players to see what they decide ... perhaps they will decide to give up on the game if it's easier for us afterward."
But it is not only the local media who are angry at Lievremont's latest selection.
Former France halfback and national team coach Pierre Berbizier, scorer of France's try in the 1987 World Cup final defeat to New Zealand, thinks Lievremont has made a mistake experimenting with Parra.
"A halfback should remain a halfback," he said. "The higher the level you play at, the more important this specificity becomes."
Denis Charvet, who won 24 caps at centre and played alongside Berbizier in the 1987 final, is increasingly confused by the current French side.
"We still have no guarantees. We're improvising with Morgan Parra at first five-eighths, we're taking Jean-Marc Doussain to play No 10 when he's a halfback, and we're not taking Frederic Michalak, who is fine form in South Africa," Charvet said on RMC radio station. "What surprises me is that we're turning this France team into a laboratory, and against the All Blacks we know we have no room for error."
Former prop Serge Simon went further still in his criticism and said the team selection "is Marc [Lievremont] through and through, [and] makes no sense." He then blamed Lievremont for "destroying Trinh-Duc['s]" confidence.
Former Wales No 8 Scott Quinnell made the following comment on his Twitter account: "Parra at 10 for France v NZ. Do you get the feeling that they would rather not win?"
France were the last visiting team to win at Eden Park, when they beat the All Blacks 23-20 in 1994.
A similar result would do wonders for French confidence, but not necessarily for their chances of reaching another final.
France would then be in first place in Pool A and face the prospect of nemesis Argentina in the quarter-finals, and Australia or South Africa in the semifinal.
- AP
