Christie, who does not have a contract with a professional club, will slot into the central midfield role. Vicelich has in the past occupied that spot in front of the back three.
Christie appeared twice for the All Whites at the last World Cup finals in South Africa and Herbert said he felt comfortable pushing him into the starting role against Mexico, who qualified for the inter-confederation playoff by finishing fourth in CONCACAF's six-nation final group.
"Jeremy is well ahead of things physically and is a player who has worked his socks off and is desperate to be part of the All Whites," Herbert said in a statement.
"His marking ability is something which will be key for us and he's well suited to the role he has been given."
The 37-year-old Vicelich has dropped back into defence after usual captain Winston Reid was ruled out with an ankle injury, allowing Smith to take the armband.
"The experience Tommy has from international level, the club he plays for and the level he plays at serves him well and he will bring those qualities to the side," Herbert added.
"But it won't all fall on one person's shoulders. We expect to have 11 leaders out there together."
Tony Lochhead, who also does not have a professional club after being released by the A-League's Wellington Phoenix last season, and Leo Bertos will act as wingbacks and drop back in defence when required.
Michael McGlinchey will provide the attacking thrust from the middle of the park, Herbert said, with Chris Wood, Kosta Barbarouses and Jeremy Brockie up front.
Herbert named the side after their final training run at the Azteca, having spent most of their buildup in Los Angeles before venturing to the Mexican capital.
"The feeling around the game here in Mexico is incredibly passionate and there has been an unbelievable volume of interest and the All Whites are part of that which is good for us," Herbert said.
"We will need to be disciplined up against a higher ranked side and our ability to maintain our shape and perform the roles which have been given will be important for us.
"Our approach is something the players know and are comfortable with and we have a history of producing in."
The second leg will be in Wellington on November 20.
New Zealand: 1-Glen Moss, 3-Tony Lochhead, 5-Tommy Smith (captain), 7-Leo Bertos, 8-Michael McGlinchey, 15-Ivan Vicelich, 16-Jeremy Brockie, 17-Kosta Barbarouses, 20-Chris Wood, 21-Jeremy Christie, 22-Andrew Durante.
Substitutes (from): 2-Jake Butler, 4-Ben Sigmund, 6-Bill Tuiloma, 9-Shane Smeltz, 10-Rory Fallon, 11-Marco Rojas, 12-Tamati Williams, 13-Chris James, 14-Storm Roux, 18-Craig Henderson, 19-Aaron Clapham, 23-Jacob Spoonley
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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