Assistant coach Ian Foster said the wing was "jumping out of his skin".
"We felt that he wasn't quite in the shape we needed him to be," Foster said. "I have to say that his attitude in dealing with it has been outstanding.
"He knows he's got a role to do in this team and that is for him to be big, strong, and powerful and to be able to step and fend. We probably saw at the end of Super Rugby that he wasn't in the shape to be able to do that.
"We made a call alongside him to use that [three-week] window to really work hard on his fitness. He's done that really well. I think he's still got a little bit to go but we've been delighted with his attitude and the results that he has got. It's fair to say that he's jumping out of his skin at the moment.
"In the playoffs, by his own admission, he was probably down a little bit. Sometimes that happens after long Super Rugby seasons - that through necessity or attrition [players have] to taper off their programmes as they go into playoffs. Some players respond to that lower load and some players don't ... Julian probably needs regular hard work."
With Savea, Piutau, Ben Smith, Israel Dagg and Nehe Milner-Skudder in the mix for the back three positions, Savea, who has scored 30 tries in 33 tests, has every right to feel he has to perform at ANZ Stadium.
Foster said he had been impressed with the way Piutau had taken his chances in a relatively unfamiliar position - he was named man of the match after last week's 27-20 victory over the Springboks at Ellis Park.
"To be fair to Julian, I don't think it [improvement] is through a fear of non-selection. I think he's determined to be a 10 out of 10 on the big stage."