He wanted both in work because Muliaina suffered a hamstring strain before the second pool game with Japan and has yet to play while Dagg needs to keep ticking over.
Two into one don't go so Dagg shifts to the wing.
Others who have yet to see any matchplay, Zac Guildford and Kieran Read, both start. Sonny Bill Williams is in midfield and Jimmy Cowan gets a 50th cap.
The selectors have persisted with their unusual bench formation of a prop, hooker and two locks. Blindside looseforward cover is restricted to Sam Whitelock swapping duties or Anthony Boric coming from the reserves while Jerome Kaino is the designated openside backup.
Meanwhile Henry batted away questions about selection sentiment, saying Muliaina was part of the squad and needed to play.
"If he plays an outstanding game things open up again doesn't it. Like Israel has been playing pretty well and got player of the day last week and played exceptionally well which is very pleasing.
"We just think he [Dagg] needs another game and the other fella [Muliaina] needs to play as well and that is the best way of playing them," he said. "It is as simple as that."
Muliaina had been an outstanding All Black for a long time.
"So it is a major challenge for both of them and good for the team."
It had been a long tournament wait, Muliaina said, and the team had set the benchmark for him to emulate or raise.
"Every time you get out there is special because you don't know when it is going to be your last," Muliaina said.
"I've just got to go out there and make sure I get another week then another week after that but first of all I have to make sure I do this week right and make it special."
The selectors wanted to keep the backbone of the team intact and ticking over, with some help from some who might be needed in case of injury or form dips later in the tournament.
Guildford had bounced back from his drinking indiscretions and been a leader on the training ground and this was his shot at offering his rugby talents. Read was ready after his midweek scare and his return would bring a world-class finish to the looseforwards although he was only likely to play about 50 minutes.
"We have to be astute about building him up for the next game," Henry said.
Victor Vito and John Afoa were victims of a selection squeeze in a 30-strong group and the balance the selectors wanted.
Richard Kahui, Cory Jane and Adam Thomson were not considered because of injury but were all expected to be ready for the playoffs.