Wing Simon Webster, who scored the Scots' only try in the 36-16 defeat by the Springboks in Durban last weekend, starts along with Leeds Tykes stand-off Gordon Ross.
The pair replace Sean Lamont, who is fit after a leg injury, and Dan Parks respectively.
Dougie Hall is named at hooker in place of Scott Lawson, while Craig Smith also starts in the front row with Bruce Douglas dropping to the bench.
Lock Alastair Kellock celebrates his 25th birthday with a call-up to the starting XV along with Jon Petrie at number eight as Allister Hogg moves to openside flanker.
Scott Murray drops out of the squad while Donnie Macfadyen is on the bench.
Hadden said: "Our first priority is to win the Test match this weekend and there are also things we need to look at from the World Cup perspective, such as the blend of the side and what individuals can do.
"Last week's group had the opportunity to do something special. Now that chance falls to the team for this week."
Scotland team to play South Africa in the second Test in Port Elizabeth on Saturday, June 17:
Hugo Southwell (Edinburgh Gunners); Chris Paterson (Edinburgh Gunners), Marcus di Rollo (Edinburgh Gunners), Andrew Henderson (Glasgow Warriors), Simon Webster (Edinburgh Gunners); Gordon Ross (Leeds Tykes), Mike Blair (Edinburgh Gunners); Gavin Kerr (Leeds Tykes), Dougie Hall (Edinburgh Gunners), Craig Smith (Edinburgh Gunners), Nathan Hines (Perpignan), Alastair Kellock (Edinburgh Gunners), Jason White (Sale Sharks, captain), Jon Petrie (Glasgow Warriors), Allister Hogg (Edinburgh Gunners).
Replacements: Scott Lawson (Glasgow Warriors), Bruce Douglas (Border Reivers), Scott MacLeod (Border Reivers), Kelly Brown (Border Reivers), Donnie Macfadyen (Glasgow Warriors), Sam Pinder (Glasgow Warriors), Ben MacDougall (Border Reivers).