The Edinburgh Gunners full-back will replace team-mate Chris Paterson, who moves to the wing for the visit of the All Blacks.
Rory Lamont has been ruled out after suffering a head injury in the 18-11 win over Samoa, prompting Paterson's switch.
Props Gavin Kerr and Bruce Douglas return to the starting XV to replace Allan Jacobsen and Craig Smith at loose-head and tight-head respectively.
Edinburgh's winger Simon Webster has earned a place on the bench for the first time in the November series.
Hadden has backed Southwell, 25, to reproduce his club form at Murrayfield.
He said: "Asking somebody to step up is a tremendous opportunity for them.
"Hugo has spent a bit of time on the wings but he got his opportunity at club level and took it with both hands. We expect him to do the same."
But the Scotland head coach admits a shortened week after the win over Samoa could hamper the team's preparations.
Hadden added: "We are really looking forward to the challenge.
"It is not ideal with a six-day turnaround - it messes up the planning - but the boys are in good spirits and looking forward to the game."
Scotland team to play New Zealand in the Autumn Test at Murrayfield on Saturday, November 26:
H Southwell (Edinburgh Gunners); C Paterson (Edinburgh Gunners), M Di Rollo (Edinburgh Gunners), A Henderson (Glasgow Warriors), S Lamont (Northampton Saints); D Parks (Glasgow Warriors), C Cusiter (Border Reivers), G Kerr (Leeds Tykes), S Lawson (Glasgow Warriors), B Douglas (Border Reivers), C Hamilton (Glasgow Warriors), S Murray (Edinburgh Gunners), J White (Sale Sharks), S Taylor (Edinburgh Gunners); A Hogg (Edinburgh Gunners).
Substitutes: D Hall (Edinburgh Gunners), C Smith (Edinburgh Gunners), A Kellock (Edinburgh Gunners), K Brown (Border Reivers), M Blair (Edinburgh Gunners), P Godman (Edinburgh Gunners), S Webster (Edinburgh Gunners).