Graham is joined in the starting line-up by Grant Gilchrist, Jamie Ritchie and Hamish Watson, while Stuart McInally, Pierre Schoeman and Blair Kinghorn are all selected among the replacements for the final Autumns Nations Series test, which kicks off at 1pm.
Scotland coach Gregor Townsend said: “This group of players have another opportunity to represent their country this weekend and show the progress we have made as a group over the past four weeks.
“Last Saturday’s defeat was a valuable – if painful – learning experience for us, and we’ve been encouraged by how well the squad has trained this week in response to the loss against South Africa
“We know how much a winning performance can lift our nation and we will be giving everything for our supporters at BT Murrayfield on Saturday.”
Stuart Hogg starts at full-back to earn his 88th cap and move into fourth position in the Scotland male all-time capped list.
In the backs Glasgow’s Sam Johnson starts at inside centre alongside Gloucester’s Chris Harris at outside-centre.
Graham and and former Edinburgh man Duhan Van Der Merwe, now at Gloucester, are selected to take up the two wing berths.
Finn Russell, starts at 10 and again partners with Ali Price at scrum-half to complete the same Scotland backline which started in the win over Australia two weeks ago.
Townsend makes five changes to the pack. Glasgow prop Jamie Bhatti earns his first Scotland start since August 2019 when he lined up against France in a pre-Rugby World Cup 2019 fixture.
He is joined in the front row by club-mate George Turner who has recovered from injury to pack down at hooker.
In a new-look back-row Josh Bayliss makes his first start for Scotland at number eight. Edinburgh flankers Ritchie and Watson resume their blindside and openside positions from the Wallabies win, with Ritchie also named as vice-captain.
There is the possibility of Scotland debuts for two players from the bench with Scarlets’ prop Javan Sebastian and Cell C Sharks back-row forward Dylan Richardson both called into the matchday 23 for the first time.