The two-time World Player of the Year was a surprising choice to start the Pool B clash in Oita on Wednesday given Hansen had chosen just two flyhalves for the World Cup and said before the tournament he might rotate them during pool matches.
Hansen, who has preferred the pair to operate in tandem as dual playmakers in recent matches, played them together in the opening match against the Springboks with Barrett at fullback.
The expectation was that only one would be in the match-day squad against Canada and for the following match against Namibia.
Hansen, however, said on Monday he wanted to give the pair as much game time as possible in tandem.
"I just want them to be on the park together," Hansen said. "They haven't had a lot of test matches together so they just need some more time.
"I'm not saying they're not clicking or anything like that, it's just time (together)."
The Barretts will become the first trio of brothers to appear for the All Blacks in a World Cup match and first trio of brothers to start a World Cup game since Elisi, Manu and Fe'ao Vunipola represented Tonga against Scotland in 1995.
The three Pisi brothers - Ken, Tusi and George - all played for Samoa against South Africa in 2015 but only Ken started that match.
Jack Goodhue has returned from a hamstring injury that kept him out for almost two months and will link with Sonny Bill Williams in the midfield.
"He doesn't need to show us he is an international rugby player, we already know that," Hansen said of Goodhue's return.
"What he needs to do is get some minutes into his legs. He hasn't played for six weeks so he may only play 30, 40, 50 minutes and it's important that he gets through that and he gets through it well."
Rieko Ioane, who has scored 23 tries in 26 tests, also returns on the left wing after being dropped for the Bledisloe Cup match against Australia in Auckland last month.
"He's in a contest against two other guys who are playing wonderful rugby," Hansen said, referring to Sevu Reece and George Bridge.
"We know that he can also play wonderful rugby. It's important that he doesn't come out and get too caught up in the contest and that he does the small things well and the big things will come for him.
"Once he does that, and I'm sure he will, the pressure will come back on to the selectors to pick him."
All Blacks team to face Canada (Test caps in brackets):
1: Atu Moli (2), 2: Liam Coltman (6), 3: Angus Ta’avao (9), 4: Patrick Tuipulotu (26), 5: Scott Barrett (32), 6: Shannon Frizell (6), 7:Matt Todd (21), 8: Kieran Read - captain (123), 9: TJ Perenara (60), 10: Richie Mo’unga (13), 11: Rieko Ioane (26), 12: Sonny Bill Williams (54), 13: Jack Goodhue (9), 14: Jordie Barrett (12), 15: Beauden Barrett (79).
Reserves
16: Codie Taylor (46), 17: Ofa Tuungafasi (31), 18: Nepo Laulala (21), 19: Samuel Whitelock (113), 20: Ardie Savea (40), 21: Brad Weber (2), 22: Ryan Crotty (46), 23: Ben Smith (81).
- Reuters and ODT Online
